There are 5 US Post Offices in Fentress County serving a total of 17,051 residents equating to 3,410 residents per post office. It's estimated that approximately 27,215 packages are handled across the 5 county post offices annually. Fentress County is a county located in the U.S. state of Tennessee. As of the 2010 census, the population was 17,959. Its county seat is Jamestown."