When you say in there I presume you mean the Civil War.
As I interpret the info William Parks in Co H, 72nd EMM, promoted to Corporal from Ozark MO may be Joshua Parks uncle. William Fred would have just been 15, not unheard of, but it would be a bit unusual.
I do believe William Fred is the soldier listed in Co H., 16th MO Cav. enlisting at age 18, Sept 1, 1864.
If you have a picture of him in uniform, the uniform itself may give the answer as he was a private in the 16th.