[1] Clayton Township is named for Kentucky statesman Henry Clay.

[3] (This list is based on USGS data and may include former settlements.)

As of the 2020 census[1] there were 958 people, 362 households, and 234 families residing in the township.

The racial makeup of the township was 93.22% White, 1.04% African American, 0.00% Native American, 0.42% Asian, 0.00% Pacific Islander, 0.63% from other races, and 4.70% from two or more races.

31.80% of all households were made up of individuals, and 14.60% had someone living alone who was 65 years of age or older.