There are 5 US Post Offices in Clay County serving a total of 8,329 residents equating to 1,666 residents per post office. It's estimated that approximately 13,294 packages are handled across the 5 county post offices annually. Clay County (county code CY) is a county located in the U.S. state of Kansas. As of the 2010 census, the county population was 8,535. Its county seat and most populous city is Clay Center."