Jamestown is a home rule-class city in Russell County, Kentucky, in the United States. It is the seat of its county. The population was 1,794 a…Jamestown is a home rule-class city in Russell County, Kentucky, in the United States. It is the seat of its county. The population was 1,794 at the 2010 U.S. census. According to the United States Census Bureau, the city has a total area of 2.2 square miles, all land.