Kevil is a home rule-class city in Ballard County, Kentucky, United States. The population was 376 at the 2010 census, down from 574 in 2000. …Kevil is a home rule-class city in Ballard County, Kentucky, United States. The population was 376 at the 2010 census, down from 574 in 2000. It is part of the Paducah micropolitan area.