Wadsworth is a city in Medina County, Ohio, United States. Founded on March 1, 1814, the city was named after General Elijah Wadsworth, …Wadsworth is a city in Medina County, Ohio, United States. Founded on March 1, 1814, the city was named after General Elijah Wadsworth, a Revolutionary War hero and War of 1812 officer who owned the largest share of the lands that became Medina County. A suburb of Akron, the population was 24,007 at the 2020 census.