Geneseo is a city in Rice County, Kansas, United States. As of the 2020 census, the population of the city was 236. For millennia, the land no…Geneseo is a city in Rice County, Kansas, United States. As of the 2020 census, the population of the city was 236. For millennia, the land now known as Kansas was inhabited by Native Americans. In 1803, most of modern Kansas was secured by the United States as part of the Louisiana Purchase. In 1854, the Kansas Territory was organized, then in 1861 Kansas became the 34th U.S. state. In 1867, Rice County was founded.