Clayton is a town in and the county seat of Union County, New Mexico, United States. As of the 2010 census, the city population was 2,980. Native Americans were present in the area of Clayton for at least 10,000 years, as evidenced by the findings at the Folsom site about 55 miles northwest of Clayton, near the village of Folsom. Later the area was …Clayton is a town in and the county seat of Union County, New Mexico, United States. As of the 2010 census, the city population was 2,980. Native Americans were present in the area of Clayton for at least 10,000 years, as evidenced by the findings at the Folsom site about 55 miles northwest of Clayton, near the village of Folsom. Later the area was part of Comancheria.