I have not been able to find a Samuel Eugene Nesbitt in the roster of any Confederate unit or the Vicksburg Parole List.

Nor is he found in the Compiled Service Records for the:

Twentieth Confederate Cavalry, N-Y AND Baxter's Battalion, Confederate Cavalry
https://www.fold3.com/image/271/119641662

Col. Lay, at the time of the Vicksburg siege of 62-63, was at the time serving as a Surgeon in Vicksburg hospitals. His 20th Confederate Cavalry is not listed in the Vicksburg Order of Battle