Hamilton County is a county in the U.S. state of New York. As of the 2010 census, 4,836 people lived there. The county seat is Lake Pleasant. The county is named after Alexander Hamilton, the only member of the New York State delegation who signed the United States Constitution in 1787 and later the first United States Secretary of the Treasury. The county was created in 1816 and organized in 1847. This county is part of New York's 21st congressional district.