Wellsville is a city in Montgomery County, Missouri, United States. The population was 998 at the 2020 census, down from 1,217 in 2010. W…Wellsville is a city in Montgomery County, Missouri, United States. The population was 998 at the 2020 census, down from 1,217 in 2010. Wellsville was platted in 1856, and named after Charles Wells who was the original owner of the land. A post office called Wellsville has been in operation since 1857.