It's not definitive but fits pretty close and at least there is a primary source to look into. From:
List of Soldiers, Serving in Units from the State of Missouri, Executed During the Civil War by U.S. Military Authorities for whom Proceedings of Court-Martial and Military Commissions have been Filmed.
(Kelso?) Paul Kingston Co. M 1st MO Cav.
(Al Purvis?) Abraham Purvis Co. C 21st MO Inf.
(Richard Underwood?) Ephraim Richardson Co. C 21st MO Inf. filed with Abraham Purvis
Extracted from: List of Soldiers Executed During the Civil War by U.S. Military Authorities for whom Proceedings of Court-Martial and Military Commissions have been Filmed; Proceedings of U.S. Army Courts-Martial and Military Commissions of Union Soldiers Executed by U.S. Military Authorities, 1861-1866 (National Archives Microfilm Publication M1523, roll 1); Records of the Adjutant General’s Office, 1780’s-1917, Record Group 94; National Archives Building, Washington, DC.
The issue of course is these 3 were all UNION soldiers executed.
Kingston from Bunker Hill Ill enlisted Jeff Barracks Sept 6 1861 hung Cape Girardeau Nov 27, 1863 for murder and desertion.
Purvis was from Scotland Co, enlisted Hannibal Feb 1864, age 18 y/o, hung St Louis Jan 13, 1865 for murder.
Richardson was from Memphis, Scotland Co, MO Nov 1862 age 16, hung St Louis Jan 13, 1865 for murder.
Could Mudd have conflated the issue? All 3 were from NE MO/east central ILL. I can't find anything at all in the records to match on the CSA or MSG side of the coin any of the 3 names.