Vernon is a town in Vernon Township, Jennings County, Indiana, United States. As of the 2010 census, the town population was 318. As the county seat of Jennings County, it is the smallest town with that designation in the state of Indiana. It is nearly surrounded by the Muscatatuck River. Vernon has the only elected mayor of a town in the state of Indiana and the only elected town marshal. Dr. Wayne Zamora is Mayor and Britt Burgmeier is the Marshal..