A Study Comparing Zasocitinib (TAK-279) With Deucravacitinib in Adults With Plaque Psoriasis

Inclusion Criteria: 1. Participant has a diagnosis of chronic plaque psoriasis for \>=6 months prior to the screening visit. 2. Participant has stable plaque psoriasis, defined as no significant flare or change in morphology (as assessed by the investigator) in psoriasis, for \>=6 months before screening. 3. Participant has moderate-to-severe plaque psoriasis, as defined by a PASI score \>=12 and an sPGA score \>=3, at screening and Day 1. 4. Participant has plaque psoriasis covering \>=10 percent (%) of his or her total body surface area (BSA) at screening and Day 1. 5. Participant must be a candidate for phototherapy or systemic therapy. Exclusion Criteria: \- Target Disease-Related Exclusions: 1. Participant has evidence of nonplaque psoriasis (erythrodermic, pustular, predominantly guttate psoriasis, predominantly inverse, or drug-induced psoriasis). If a participant meets criteria for inclusion based on typical plaque psoriasis presentation, a limited amount of inverse psoriasis is not exclusionary. 2. Participant requires systemic treatment, other than nonsteroidal anti-inflammatory drugs, during the trial period for an immune related disease (for example, inflammatory bowel disease). 3. Participant has a history of excessive sun exposure, has used tanning booths within 4 weeks prior to Day 1, or is not willing to minimize natural and artificial sunlight exposure during the trial period. Use of sunscreen products and protective apparel is recommended when sun exposure cannot be avoided. 4. Participant has concomitant comorbid skin condition that, in the opinion of the investigator, would interfere with the trial assessments. Recent/Concurrent Infectious Disease Exclusions: 5. Tuberculosis (TB): 1. Participant has history of active TB infection, regardless of treatment status. 2. Participant has signs or symptoms of active TB (including, but not limited to, chronic fever, chronic productive cough, night sweats, or weight loss) as judged by the investigator. 3. Participant has evidence of latent TB infection (LTBI) as evidenced by a positive QuantiFERON-TB Gold (QFT) result OR 2 indeterminate QFT results, and participant does not have documentation of appropriate LTBI prophylaxis or is not able or not willing to initiate appropriate LTBI prophylaxis. 4. Participant has had any imaging trial during or 6 months prior to screening, including x-ray, chest computed tomography, Magnetic Resonance Imaging (MRI), or other chest imaging suggesting evidence of current active or a history of active TB. X-ray is required for all participants regardless of QFT results unless the participant has had normal chest imaging in the 6 months prior to screening. 6. Herpes infections: 1. Participant has active herpes virus infection, including herpes zoster or herpes simplex 1 and 2 (demonstrated on physical examination and/or medical history) at screening or Day 1. 2. Participant has history of serious herpetic infection that includes any episode of disseminated disease, multidermatomal herpes zoster, herpes encephalitis, ophthalmic herpes, or recurrent herpes zoster (defined as 2 episodes within 2 years). 7. Nonherpetic viral diseases: 1. Participant has presence of Hepatitis C Virus (HCV) antibody and a positive confirmatory test result for HCV ribonucleic Acid (RNA) (nucleic acid test or Polymerase Chain Reaction \[PCR\]). 2. Participant has presence of positive Hepatitis B Surface Antigen (HBsAg+), or indeterminate HBsAg, presence of HBV deoxyribonucleic Acid (DNA) (regardless of serology), or positive anti-hepatitis B core antibody without concurrent positive hepatitis B surface antibody (Hepatitis B Core Antibody \[HBcAb\] positive and Hepatitis B Surface Antibody \[HBsAb\] negative). 3. Participant has positive results for Human Immunodeficiency Virus (HIV) by serology, regardless of viral load. 8. Other infectious diseases: 1. Participant has a history of active infection or febrile illness within 7 days prior to Day 1, as assessed by the investigator. 2. Participant has history of symptoms suggestive of systemic or invasive infection within 30 days prior to Day 1. 3. Participant has history of bacterial, viral, or fungal infection that required hospitalization or treatment with intravenous antimicrobial therapy within 8 weeks prior to Day 1 or oral antimicrobial therapy within 30 days prior to Day 1. 4. Participant has a history of chronic or recurrent bacterial disease, including but not limited to chronic pyelonephritis or cystitis, chronic bronchitis/pneumonitis, osteomyelitis, or chronic skin ulcerations/infections or fungal infections (except superficial onychomycosis). 5. Participant has a history of an infected joint prosthesis, unless that prosthesis has been removed or replaced at least 60 days prior to Day 1. 6. Participant has a history of opportunistic infections (for example, Pneumocystis jirovecii pneumonia, histoplasmosis, coccidiomycosis). 7. Participant had a bacterial infection within 60 days prior to Day 1 for which he or she did not receive treatment. * Noninfectious Disorders Exclusions: 9. Participant has any clinically significant medical condition, evidence of an unstable clinical condition (for example, cardiovascular, renal, hepatic, hematologic, gastrointestinal, endocrine, pulmonary, or immunologic), or vital signs/physical/laboratory/Electrocardiogram (ECG) abnormality that would, in the opinion of the investigator, put the participant at undue risk or interfere with interpretation of trial results. These include but are not limited to: 1. Participant has a history of known or suspected condition/illness that is consistent with compromised immunity, including but not limited to any identified congenital or acquired immunodeficiency, splenectomy. 2. Participant had a major surgery within 60 days prior to Day 1 or has a major surgery planned during the trial. 3. Participant has unstable, poorly controlled, or severe hypertension at screening, confirmed by 2 repeat assessments. 4. Participant has a history of Class III or IV congestive heart failure as defined by New York Heart Association criteria. 5. Participant has a history of cancer or lymphoproliferative disease, with the exception of successfully treated nonmetastatic cutaneous squamous cell or basal cell carcinoma and/or localized carcinoma in situ of the cervix. 6. For participants with asthma, chronic obstructive pulmonary disease, or other pulmonary illnesses, participant has been hospitalized in the past 3 months, has ever required intubation for treatment, currently requires oral corticosteroids, or has required more than 1 course of oral corticosteroids within 6 months prior to Day 1. 7. Participant has any of the following cardiovascular disease history: * A new diagnosis of atrial fibrillation or an episode of atrial fibrillation with rapid ventricular response or other dysrhythmia, nonacute cardiac hospitalization (for example, pacemaker implantation), pulmonary embolism, or deep venous thrombosis within the past 6 months prior to screening. * Any history of cerebrovascular event, myocardial infarction, coronary stenting, or aorto-coronary bypass surgery. If, however, the investigator determines there are no suitable treatment alternatives available for the participant and it has been at least 6 months since the occurrence of any such event, the participant may enroll. 8. Participant has ECG abnormalities that are considered clinically significant and would pose an unacceptable risk to the participant if he or she participated in the trial, in the opinion of the investigator. 9. Participant has significant/uncontrolled psychiatric illness, in the opinion of the investigator. 10. Participant has a history of clinically significant drug or alcohol abuse within 12 months prior to Day 1. * Prohibited Psoriasis Treatments Exclusions: For the below prohibited psoriasis treatments, the washout period prior to Day 1 is within the time frame indicated or 5 half-lives, whichever is longer, regardless of whether they are prescribed for psoriasis or another condition: 10. Participant has received any of the following biologics or biosimilar versions within the time frame indicated: 1. Antibodies to interleukin (IL)-12/-23, IL-17, or IL-23 (for example, ustekinumab, secukinumab, tildrakizumab, ixekizumab, or guselkumab) within 6 months prior to Day 1. 2. Tumor Necrosis Factor (TNF) inhibitor(s) (for example, etanercept, adalimumab, infliximab, or certolizumab) within 2 months prior to Day 1. 3. Agents that modulate integrin pathways to impact lymphocyte trafficking (for example, natalizumab) or agents that modulate B cells or T cells (for example, alemtuzumab, abatacept, or visilizumab) within 3 months prior to Day 1. 4. Rituximab or other immune cell-depleting therapy within 6 months prior to Day 1. 11. Participant has used medicated shampoo and/or body wash, including formulations containing but not limited to salicylic acid, corticosteroids, coal tar, vitamin D3 analogues, or other compounds used for the management of psoriasis within 2 weeks prior to Day 1. 12. Participant has used any topical medication that could affect psoriasis presentation (including but not limited to corticosteroids, salicylic acid, urea, alpha- or beta-hydroxy acids, anthralin, retinoids, vitamin D analogues \[such as calcipotriol\], methoxsalen, trimethylpsoralen, calcineurin inhibitors \[for example, tacrolimus\], tapinarof, roflumilast, Janus kinase (JAK) inhibitors, or tar) within 2 weeks prior to Day 1. 13. Participant has used any systemic nonbiologic treatment that could affect psoriasis presentation (including oral, intravenous, intramuscular, intra-articular, intrathecal, or intralesional corticosteroids; oral retinoids; immunosuppressive/immunomodulating medication; methotrexate; azathioprine; 6-thioguanidine; mercaptopurine; mycophenolate mofetil; hydroxyurea; cyclosporine; 1,25-dihydroxyvitamin D3 analogues; psoralens; sulfasalazine; fumaric acid derivatives; JAK inhibitors; apremilast) within 4 weeks prior to Day 1, or 5 half-lives, whichever is longer. Note: Intranasal corticosteroids, inhaled corticosteroids, and eye and ear drops containing corticosteroids are permitted. 14. Participant has used leflunomide within 6 months prior to Day 1. 15. Participant has received phototherapy (including Ultraviolet B \[UV B\], Psoralen plus Ultraviolet A \[PUVA\], tanning beds, therapeutic sunbathing) or excimer laser within 4 weeks prior to Day 1. 16. Participant has used botanical preparations (for example, herbal supplements or traditional medicines, including traditional Chinese medicines derived from plants, minerals, or animals) intended to treat psoriasis or other immunological diseases within 4 weeks prior to Day 1. 17. Participant is currently being treated with oral antihistamines for any reason, with the exception of oral antihistamines that are administered at a stable dose for at least 4 weeks prior to Day 1. Note: Additional treatment with oral antihistamines may be permitted after discussion with the medical monitor. 18. Participant has any previous exposure to zasocitinib (also known as TAK-279 or NDI 034858) or other Tyrosine Kinase 2 (TYK2) inhibitors (including deucravacitinib), or participated in any trial that included a TYK2 inhibitor (for example, deucravacitinib, VTX958, GLPG3667, et cetera), unless participant has documentation of posttrial unblinding that confirms the participant did not receive a TYK2 inhibitor. \- Other Prohibited Concomitant Medications Exclusions: For the below prohibited concomitant medications, where applicable, the washout period prior to Day 1 is within the time frame indicated or 5 half-lives, whichever is longer. 19. Participant has received lithium, antimalarials, or intramuscular gold therapy within 4 weeks prior to Day 1. 20. Participant is currently being treated with strong or moderate Cytochrome P450 3A4 (CYP3A4) inhibitors (such as itraconazole) or strong or moderate CYP3A4 inducers (such as rifampin, carbamazepine, or phenytoin), or has received strong or moderate CYP3A4 inhibitors or strong or moderate CYP3A4 inducers within 4 weeks or 5 half-lives of the inducer or inhibitor, whichever is longer, prior to Day 1, or is anticipated to require treatment with strong or moderate CYP3A4 inducers or inhibitors during the trial period. Note: This includes consumption of food or beverages containing grapefruit and/or Seville oranges within 1 week of Day 1. Participants must be counseled to avoid food or beverages containing grapefruit and/or Seville oranges for the duration of the trial. 21. Participant has received any live-attenuated vaccine within 60 days prior to Day 1 or plans to receive a live-attenuated vaccine during the trial and up to 4 weeks after the last trial intervention administration. Note: Non-live-attenuated vaccines or boosters for Coronavirus Disease 2019 (COVID-19) or influenza are permitted during the trial. 22. Participant received an investigational antibody or biologic therapy within 6 months prior to Day 1. 23. Participant received an investigational oral therapy within 3 months prior to Day 1. 24. Participant is currently receiving a nonbiological trial intervention or device or has received one within 4 weeks prior to Day 1. 25. Participant is currently enrolled in a clinical trial or anticipates enrollment in a clinical trial during the course of the trial. \- Laboratory/Physical Exclusions: 26. Participant has any of the following laboratory values at the screening visit: 1. Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) values greater than (˃)3\*upper limit of normal (ULN). 2. Total Bilirubin (Tbili) (unconjugated and/or conjugated) ˃1.5\*ULN. 3. Hemoglobin less than (\<) 9.0 grams per deciliter (g/dL) (\<90.0 grams per liter \[g/L\]). 4. Absolute white blood cell (WBC) count \<3.0\*109/liters (L) (\<3000 per cubic millimeter \[/mm3\]). 5. Absolute neutrophil count of \<1.0\*109/L (\<1000/mm3). 6. Absolute lymphocytes count of \<0.5\*109/L (\<500/mm3). 7. Platelet count \<100\*109/L (\<100,000/mm3). 8. Thyroid-stimulating hormone outside the normal reference range AND free T4 or T3 outside the normal reference range. 9. Estimated creatinine clearance \<45 milliliters per minute (mL/min) based on the Cockcroft-Gault calculation. 10. Creatine phosphokinase (CPK) \> ULN. CPK may be repeated once; if repeat value is Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 or lower (or \<=2.5\*ULN) and no higher than the initial value, participant remains eligible. Investigators should assess the participant for modulating factors, including concomitant medications or vigorous exercise, that may affect CPK levels. 27. Participant has any other significant laboratory abnormalities that, in the opinion of the investigator, might place the participant at unacceptable risk for participation in this trial. 28. Participant does not tolerate venipuncture or inability to be venipunctured. \- Allergies and Adverse Drug Reactions Exclusions: 29. Participant has history of significant drug allergy (such as anaphylaxis). 30. Participant has a known or suspected allergy to zasocitinib or deucravacitinib or any of their components.