Psoriatic arthritis (PsA) is a long-term illness causing joint pain and skin issues in people with psoriasis (PsO). This study focuses on people with active PsA who haven't tried biologic medicines yet. Participants will receive either a medicine called **zasocitinib**, another active treatment, or a **placebo** (a dummy pill with no medicine). The study lasts up to 60 weeks. **Key Points:** - Participants will stay in the study for up to 60 weeks. - You must be 18 or older and have PsA for at least 3 months to join. - People with other diseases like rheumatoid arthritis or lupus cannot participate. To join, you must have signs of PsA, like tender and swollen joints or psoriasis skin spots. If you've tried and not responded well to certain arthritis medicines before, you might be eligible. The study aims to see how effective zasocitinib is in treating PsA. Participants with other skin conditions or illnesses like fibromyalgia cannot join.