Salyersville is a home rule-class city on the Licking River in Magoffin County, Kentucky, in the United States. It is the seat of its county. As …Salyersville is a home rule-class city on the Licking River in Magoffin County, Kentucky, in the United States. It is the seat of its county. As of the 2020 census, the population was 1,591, down from 1,883 in 2010.