Clinton County is a rural county in south-central Kentucky along the Cumberland River. Known for affordable land prices, minimal zoning restrictions, and strong agricultural use, Clinton County is popular with homesteaders and off-grid buyers. County seat: Albany. The Eastern Kentucky county of Leslie, with Hyden as its seat and a population of about 10,120, is characterized by its deep hollows and forested mountains, presenting a unique opportunity for land buyers looking for remote, unspoiled terrain ideal for off-grid living and self-sufficiency.