This kind of hat is called a shako. It was worn by a group of militiamen known as the Lexington Rifles. The group was created by John Hunt Morgan. The Lexington Rifles was one of the first militia groups to leave Kentucky and join the Confederacy. They caused the Union a lot of trouble. They devastated supply lines, raided towns, captured horses, and disrupted Union forces.
This resource is part of the A State Divided: Exploring the Civil War Through Images collection.