Geneva is a city in, and the county seat of, Fillmore County, Nebraska, United States. The population was 2,217 at the 2010 census. Genev…Geneva is a city in, and the county seat of, Fillmore County, Nebraska, United States. The population was 2,217 at the 2010 census. Geneva was founded in 1871. It was named after Geneva, in Switzerland, perhaps via Geneva, New York.