Genesee Falls is an incorporated town in Wyoming County, New York. The population was 438 at the 2010 census. The Town of Genesee Falls is in the southeastern corner of the county. The Town of Genesee Falls was established in 1846. The town was created from part of the Town of Pike and from part of the Town of Portage in Livingston County, New …Genesee Falls is an incorporated town in Wyoming County, New York. The population was 438 at the 2010 census. The Town of Genesee Falls is in the southeastern corner of the county. The Town of Genesee Falls was established in 1846. The town was created from part of the Town of Pike and from part of the Town of Portage in Livingston County, New York.