A Phase II, Single-center, Single-arm Study Evaluating the Safety and Efficacy of Golidocitinib in the Management of Newly Diagnosed Peripheral T Cell Lymphoma Patients (GOLDEN Study) and Correlative Study

Inclusion Criteria: * Provision of a signed and dated, written informed consent form prior to any study specific procedures, sampling, and analyses. * Submission of the tumor block or unstained slides from an excisional or core biopsy from nodal or extra-nodal lymphoma tissue (archived or newly obtained sample) is required for retrospective central confirmation of tumor histological subtype. * Aged ≥ 18 years old. * Participants must exhibit Eastern Cooperative Oncology Group (ECOG) performance status 0-2 with no deterioration over the previous 2 weeks. * Predicted life expectancy ≥ 12 weeks. * Participants must have histologically confirmed peripheral T-cell lymphoma by MD Anderson pathology review according to the 2016 revision of the World Health Organization classification of lymphoid neoplasms53. Eligible histological subtypes are restricted to the following: * PTCL, not otherwise specified (PTCL, NOS) (the proportion of PTCL-NOS subtype will not exceed 30% of all enrolled) * Angioimmunoblastic T-cell lymphoma (AITL) * Follicular T cell lymphoma * PTCL with T follicular helper (TFH) phenotype * Participants must have measurable disease according to the 2014 Lugano classification, which is defined as lymphomatous nodes, nodal masses, or other lymphomatous lesions are measurable in two diameters (longest diameter \[LDi\] and shortest diameter perpendicular to the LDi \[SDi\]) on CT scans, and also with LDi as below: * A measurable node must have an LDi greater than 1.5 cm. * A measurable extranodal lesion should have an LDi greater than 1.0 cm. * Participants must be treatment naïve with no prior systemic treatment for T-cell lymphoma (i.e., PTCL). Participants could be transplant eligible or ineligible upon their entries to this study. * Adequate bone marrow reserve and organ system functions, as outlined below: * Absolute neutrophil count (ANC) ≥ 1 ×109/L (≥0.5 ×109/L if documented bone marrow involvement with lymphoma) independent of growth factor support within 7 days of study entry. * Platelets ≥ 75 × 109/L (or ≥ 50 × 109/L if documented bone marrow involvement with lymphoma) independent of growth factor support or transfusion within 7 days of study entry. * Hemoglobin ≥ 8 g/dL * Total bilirubin ≤ 1.5 ×ULN if no liver involvement or ≤ 3 ×ULN in the presence of documented Gilbert's Syndrome (unconjugated hyperbilirubinemia) or liver involvement. * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 × ULN, or ≤ 5 ×ULN if with document hepatic involvement with lymphoma. * Creatinine ≤ 1.5 × ULN, OR calculated or measured creatinine clearance ≥ 50 mL/min as calculated by the Cockcroft-Gault method, or 24-hour measured urine creatinine clearance ≥ 50 mL/min. * LVEF ≥ 50% assessed by ECHO or MUGA. * Participants should have the ability and willingness to comply with the study and follow up. * The effects of golidocitinib on the developing human fetus are unknown. For this reason and because JAK1 inhibitor agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. This includes all female patients, between the onset of menses (as early as 8 years of age) and 55 years unless the participants presents with an applicable exclusionary factor which may be one of the following: * Postmenopausal (no menses in greater than or equal to 12 consecutive months). * History of hysterectomy or bilateral salpingo-oophorectomy. * Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy). * History of bilateral tubal ligation or another surgical sterilization procedure. * Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Women treated or enrolled on this protocol must agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of golidocitinib administration. If female patients wish to mother children, they should be advised to arrange for freezing of eggs prior to the start of study treatment. * Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of golidocitinib administration. Men must refrain from donating sperm during their participation in the study and at least for 6 months after the last treatment. If male patients wish to father children, they should be advised to arrange for freezing of sperm samples prior to the start of study treatment. Exclusion Criteria: Participants must not enter the study if any of the following exclusion criteria are fulfilled: * Intervention with any of the following: * Any investigational anti-cancer agents or anti-cancer study drugs from a previous clinical study. * Any cytotoxic chemotherapy from a previous treatment regimen. * Corticosteroids at dosages equivalent to prednisone \> 40 mg/day within 7 days of the start of the study treatment. * Major surgery procedure (excluding placement of vascular access), or significant traumatic injury within 4 weeks of the first dose of study treatment, or have an anticipated need for major surgery during the study. * Prior treatment with a JAK or STAT3 inhibitor. * Prior treatment with any onco-immunotherapy in 28 days prior to first dosing of golidocitinib (e.g., immune checkpoint inhibitors PD-1, PD-L1, CTLA4). * Live vaccines within 28 days prior to first dose. * Participants currently receiving (or unable to stop use at least 1 week prior to receiving the first dose) medications or herbal supplements known to be Potent inhibitors or inducers of CYP3A . * Central nervous system or leptomeningeal lymphoma given the lack of evidence of CNS penetrance of the investigational drug. * Participants with severely decreased lung function (i.e. any parameter of FEV1, and DLCO \< 60% of predicted value). Past medical history of pneumonitis, drug-induced interstitial lung disease, radiation pneumonitis which required steroid treatment, or any evidence of clinically active interstitial lung disease. * Participants with disease condition which requires the treatment of immunosuppressants, biologics, or NSAIDs (non-steroid anti-inflammatory drugs). * Active infections including * History of known active tuberculosis (TB). * Known infection with human immunodeficiency virus (HIV). * Known active hepatitis B or hepatitis C infection as follows * Active viral infections (i.e., zoster) other than hepatitis B or C. o Infections requiring oral or intravenous antimicrobial therapy or interferon within 14 days. * Any of the following cardiac criteria: * Congestive heart failure (CHF) per New York Heart Association (NYHA) classification \> Class II . * Clinically significant valvular diseases, hypertrophic or constrictive cardiomyopathy. * Any clinically significant abnormalities in rhythm, conduction or morphology of resting ECG, e.g., complete left bundle branch block, third degree heart block, and second-degree heart block, PR interval \> 250 msec. * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy. * Acute Myocardial Infarction (AMI) within 6 months prior to starting treatment, unstable angina or new-onset angina. * Participants with heart transplant. * Mean resting corrected QTcF interval \>450 ms on screening electrocardiogram (ECG). * Participants with factors that increase the risk of QT prolongation or arrhythmic events (e.g., congenital long QT syndrome, any concomitant medication known to prolong the QT interval or family history of long QT interval syndrome or unexplained sudden death under 40 years of age in first degree relatives). * Participants with acute thrombotic diseases such as pulmonary embolism (PE) and deep venous thrombosis (DVT) within 90 days. Participants with remote history (\>6 months) of provoked PE or DVT (e.g., line-associated DVT; DVT or PE after surgical procedure), and participants on appropriate anticoagulation for 90 or more days from the event will not be excluded. * Another malignancy within 5 years prior to enrollment with the exception of adequately treated in-situ carcinoma of the cervix, uterus, basal or squamous cell carcinoma or non-melanomatous skin cancer. * Refractory nausea and vomiting if not controlled by supportive therapy, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection that would preclude adequate absorption of golidocitinib. * History of hypersensitivity to active or inactive excipients of golidocitinib or drugs with a similar chemical structure or class. * As judged by the investigator, any evidence of severe or uncontrolled systemic diseases, including uncontrolled hypertension or active bleeding diatheses. Screening for chronic conditions is not required. * Concurrent conditions that in the investigator's opinion would jeopardize compliance with the protocol. * Psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol. * All participants must avoid concomitant use of medications, herbal supplements and/or ingestions of foods with known potent inducer/inhibitory effects on CYP3A activity whenever feasible. Such drugs must have been discontinued for an appropriate period before they enter screening and for a period after the last dose of golidocitinib. Guidance on medications to avoid, medications that require close monitoring and on washout periods. * Participants with psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study because golidocitinib is a JAK1 inhibitor agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with golidocitinib, breastfeeding should be discontinued if the mother is treated with golidocitinib. These potential risks may also apply to other agents used in this study.