A Study to Test Different Doses of BI 730357 and Find Out Whether They Reduce Symptoms in People With Active Psoriatic Arthritis

Inclusion Criteria: * Age ≥ 18\* years and ≤ 75 years at screening, males or females \-- Except in countries where the minimum age of consent is greater than 18, in which case the minimum age is the minimum age of consent. * Signed and dated written informed consent in accordance with International Conference on Harmonisation-Good Clinical Practice (ICH-GCP) and local legislation prior to admission to the trial * Have Psoriatic Arthritis (PsA) symptoms for ≥ 6 months prior to screening, as assessed by the investigator * Have PsA on the basis of the Classification Criteria for Psoriatic Arthritis (CASPAR) with peripheral symptoms at screening visit, as assessed by the investigator * Have ≥ 3 tender joints and ≥ 3 swollen joints at screening and randomisation visits, as assessed by the investigator * At least one Psoriasis (PsO) skin or nail lesion or a documented personal history of PsO at screening, as assessed by the investigator * If patients receive concurrent PsA treatments, these need to be on stable doses as below: * For patients receiving Methotrexate (MTX): patient has received treatment for ≥ 3 months, with stable dose and stable route of administration for ≥ 4 weeks prior to randomisation to End Of Observation (EOO); patients on MTX should be taking folic acid supplementation according to local standard of care before randomisation and during the trial to minimize the likelihood of MTX associated toxicity * For patients receiving oral corticosteroids: the patient must be on a stable dose for ≥ 2 weeks prior to randomisation to EOO * For patients receiving non-steroidal anti-inflammatory drugs (NSAIDs) or paracetamol/acetaminophen Pro re nata (PRN): the patient must be on stable dose for ≥ 2 weeks prior to randomisation to EOO * Women of child-bearing potential (A woman is considered of childbearing potential, i.e., fertile, following menarche and until becoming postmenopausal unless permanently sterile. Permanent sterilisation methods include hysterectomy, bilateral salpingectomy and bilateral oophorectomy. Tubal ligation is NOT a method of permanent sterilisation. A postmenopausal state is defined as no menses for 12 months without an alternative medical cause.) must be ready and able to use highly effective methods of birth control per ICH M3 (R2) that result in a low failure rate of less than 1% per year when used consistently and correctly. Such methods should be used throughout the study and the patient must agree to periodic pregnancy testing during participation in the trial. There are no specific contraceptive requirements for male participants. Patients (males or females) following the national regulatory guidelines regarding contraception if receiving MTX as background therapy. Exclusion Criteria: * Major chronic inflammatory or connective tissue disease other than PsA (e.g. rheumatoid arthritis, systemic lupus erythematosus, ankylosing spondylitis, Lyme disease, gout) or fibromyalgia, as assessed by the investigator * Active uveitis or uveitis within 4 weeks prior to randomisation, assessed by the investigator * Suspected or diagnosed inflammatory bowel disease, assessed by the investigator * Previous exposure to BI 730357 * Prior use of any therapeutic agent directly targeted to Interleukin (IL)-12/23, IL-23 or IL-17 * Prior use of more than two different Tumor necrosis factor inhibitor (TNFi) agents * Use of the following treatments: * TNFi agents (including, infliximab, adalimumab, certolizumab pegol or golimumab) within 8 weeks prior to randomisation * Etanercept within 4 weeks prior to randomisation * Leflunomide without cholestyramine wash-out within 8 weeks prior to randomisation * Systemic non-biologic medications for PsA or PsO (including traditional Disease-Modifying Antirheumatic Drugs (DMARDs) apremilast, a Janus Kinase (JAK) inhibitor or leflunomide with cholestyramine wash-out) or photochemotherapy within 4 weeks prior to randomisation * Intraarticular injections (including steroids) and intramuscular or intravenous corticosteroid treatment within 4 weeks prior to randomisation * Topical PsO medications and phototherapy within 2 weeks prior to randomisation * Low and high potency opioid analgesics (e.g. tramadol, methadone, hydromorphone, morphine) within 2 weeks prior to randomisation * Live vaccination ≤ 12 weeks prior to randomisation, or any plan to receive a live vaccination during the conduct of this study. Bacillus Calmette-Guérin (BCG) vaccination is restricted 1 year prior to randomisation through EOO visit. * further exclusion criteria apply