Civil War era Union Discharge papers

Did individual discharge papers from the Union Army exist from this period? How would I find discharge papers of two great-granfathers that served during the time of the civil war? William A. Chariton, N.Y. 95th Inf. Mustered out 6/1865 near Washington DC and John A. Aite mustered 2nd US Cavalry, mustered out at Fort Laramie 10 July 1867?