Clayton is a town in Custer County, Idaho, United States. The population was 7 at the 2010 census, down from 27 in 2000. It is adjacent to th…Clayton is a town in Custer County, Idaho, United States. The population was 7 at the 2010 census, down from 27 in 2000. It is adjacent to the Salmon River. Clayton was founded in 1881 as a smelter site for the nearby mines.