Fairfield is a home rule-class city in Nelson County, Kentucky, in the United States. The population was 113 at the 2010 census. Originall…Fairfield is a home rule-class city in Nelson County, Kentucky, in the United States. The population was 113 at the 2010 census. Originally known as Turkey Town, Fairfield was established by the state assembly in 1818 and incorporated as a city in 1870.