**Study Summary** This study tests a new medicine called *maridebart cafraglutide* for people with **Obstructive Sleep Apnea (OSA)**. OSA is a condition where breathing stops and starts during sleep. Participants will be compared to those taking a *placebo* (a pill with no medicine) over 52 weeks. Everyone in the study uses a machine called **Positive Airway Pressure (PAP) therapy** to help them breathe better at night. The study focuses on people who are overweight or obese. **Eligibility:** To join, you must have tried losing weight before, have a body mass index (BMI) of at least 27, and use PAP therapy for at least 3 months. You cannot join if you've had certain surgeries, have other breathing problems, or use treatments besides PAP therapy. **Key Points:** - **Duration:** The study lasts for 52 weeks. - **Participation:** Must continue using PAP therapy. - **Risks:** Consider your health history and ability to follow the study requirements. This study helps researchers understand if the new medicine is safe and works well for people with OSA.