Poteet is a city in Atascosa County, Texas, United States. The population was 2,795 as of the 2020 census. It is part of the San Antonio Metrop…Poteet is a city in Atascosa County, Texas, United States. The population was 2,795 as of the 2020 census. It is part of the San Antonio Metropolitan Statistical Area. It was named for its first postmaster, Francis Marion Poteet. It is best known as the birthplace of country music legend George Strait.