This study looks at a new treatment called **radioligand therapy** for patients whose prostate cancer has come back after surgery. In this treatment, a special drug with a radioactive part called **177Lu-rhPSMA-10.1** is used to target and kill cancer cells. This drug sticks to cancer cells and delivers radiation directly to them without harming normal cells. Patients will first receive **external beam radiotherapy** (EBRT), which uses high-energy rays to shrink tumors. After that, they will get the radioligand therapy through an IV. The study is testing how safe and effective this treatment is and finding the best dose. Patients will be monitored with scans and blood tests. They will return for a follow-up visit 6 weeks after the last treatment.

• The study involves multiple visits for treatment and follow-up.
• Participants will undergo imaging tests and blood draws throughout the study.
• There are specific eligibility criteria that must be met to participate in the study.