Columbia is a home rule-class city just above Russell Creek in Adair County, Kentucky, United States. The population was 4,452 at the 20…Columbia is a home rule-class city just above Russell Creek in Adair County, Kentucky, United States. The population was 4,452 at the 2010 census. Columbia is the seat of its county. The area was settled c. 1802 by Daniel Trabue. The post office was opened on April 1, 1806, by John Field, who also ran the local store.