Mosby is a city in Clay County, Missouri, United States, along the Fishing River. The population was 101 at the 2020 census. It is part of the Ka…Mosby is a city in Clay County, Missouri, United States, along the Fishing River. The population was 101 at the 2020 census. It is part of the Kansas City metropolitan area. A post office called Mosby was established in 1887, and remained in operation until 1999. The city was named after A. G. Mosby, the original owner of the site.