Clay County is a county in the U.S. state of Nebraska. As of the 2020 United States Census, the population was 6,104. Its county seat is Clay Center. The county was formed in 1855, and was organized in 1871. It was named for Henry Clay, a member of the United States Senate from Kentucky, who went on to become United States Secretary of State. I…Clay County is a county in the U.S. state of Nebraska. As of the 2020 United States Census, the population was 6,104. Its county seat is Clay Center. The county was formed in 1855, and was organized in 1871. It was named for Henry Clay, a member of the United States Senate from Kentucky, who went on to become United States Secretary of State. In the Nebraska license plate system, Clay County is represented by the prefix 30.