Psoriatic arthritis (PsA) is a long-lasting disease where the immune system causes swelling and pain in the joints and skin of people with psoriasis (PsO), a skin condition. This study is testing a new medicine called zasocitinib (also known as TAK-279) to see how well it helps people with active PsA. Some participants will receive zasocitinib, while others will get a placebo (a fake treatment) to compare the results. The study lasts up to 60 weeks. **Key Points:** - **Length of Study:** Participants will be involved for about 60 weeks. - **Treatment:** Participants will either receive zasocitinib or a placebo. - **Eligibility:** Participants must be 18 or older, diagnosed with PsA, and show active symptoms. To join, you should have PsA symptoms for at least 3 months and meet certain health conditions. You should not have other diseases or skin conditions that could mix up the results. This study helps to understand if zasocitinib can be a helpful treatment for PsA.