Adamsville is a village in Muskingum County, Ohio, United States. The population was 140 at the 2020 census. It is part of the Zanesville micropolitan area. Adamsville was laid out in 1832 and named after John Quincy Adams or according to another source, Mordecai Adams, the proprietor of the village. A post office called Adamsville has been in o…Adamsville is a village in Muskingum County, Ohio, United States. The population was 140 at the 2020 census. It is part of the Zanesville micropolitan area. Adamsville was laid out in 1832 and named after John Quincy Adams or according to another source, Mordecai Adams, the proprietor of the village. A post office called Adamsville has been in operation since 1837. The village was incorporated in 1864.