Jesup is a city in Wayne County, Georgia, United States. The population was 9,809 at the 2020 census. The city is the county seat of Wayne …Jesup is a city in Wayne County, Georgia, United States. The population was 9,809 at the 2020 census. The city is the county seat of Wayne County. By February 1869, Willis Clary had begun building a two-story hotel near the junction of Macon and Brunswick Railroad and the Atlantic and Gulf Railroad and four stores had sprung up in the area. Clary became a driving force for the establishment of what would become Jesup and was its first mayor.