Fultonham is a village in Muskingum County, Ohio, United States.Fultonham was named for Robert Fulton, inventor of the first commercially successful steamboat.[5][6] A post office called Uniontown was established in 1818, and the name was changed to Fultonham in 1828.[7] According to the United States Census Bureau, the village has a total area of 0.16 square miles (0.41 km2), all land.The racial makeup of the village was 98.01% White, 1.32% African American, and 0.66% from two or more races.