Zanesfield is a village in Logan County, Ohio, United States of America. The population was 194 at the 2020 census. It is the smallest incorpo…Zanesfield is a village in Logan County, Ohio, United States of America. The population was 194 at the 2020 census. It is the smallest incorporated village in Logan County. Zanesfield is named for Isaac Zane, who was born in 1753 in what was then Berkeley County, Virginia, and is now Hardy County, West Virginia. He was the youngest brother of Ebenezer Zane, for whom Zanesville, Ohio, is named.