Sutton is a town in Braxton County, West Virginia, United States. The population was 876 at the 2020 census. It is the county seat of Braxton County. Sutton is situated at a center of transportation in West Virginia. Interstate 79, a major north–south route, connects with Appalachian Corridor L, another significant north–south route, passes several mile…Sutton is a town in Braxton County, West Virginia, United States. The population was 876 at the 2020 census. It is the county seat of Braxton County. Sutton is situated at a center of transportation in West Virginia. Interstate 79, a major north–south route, connects with Appalachian Corridor L, another significant north–south route, passes several miles south of town.