Allegany County is a county in the U.S. state of New York. As of the 2020 census, the population was 46,456. Its county seat is Belmont. Its name derives from a Lenape word, applied by European-American settlers of Western New York State to a trail that followed the Allegheny River; they also named the county after this. The county is part of the Western N…Allegany County is a county in the U.S. state of New York. As of the 2020 census, the population was 46,456. Its county seat is Belmont. Its name derives from a Lenape word, applied by European-American settlers of Western New York State to a trail that followed the Allegheny River; they also named the county after this. The county is part of the Western New York region of the state.