There are 9 US Post Offices in Yates County serving a total of 24,910 residents equating to 2,768 residents per post office. It's estimated that approximately 39,759 packages are handled across the 9 county post offices annually. Yates County is a county located in the U.S. state of New York. As of the 2010 census, the population was 25,348, making it the third-least populous county in New York. The county seat is Penn Yan. The name is in honor of Joseph C. Yates, who as Governor of New York signed the act establishing the county. Yates County is included in the Rochester, NY Metropolitan Statistical Area."