NPS-CWS&SS shows:

Jeremiah Fairburn
Regiment Name 41st Batt'n Virginia Cavalry (White's Battalion)
Side Confederate
Company B
Soldier's Rank_In Private
Soldier's Rank_Out Private
Film Number M382 roll 18

Co B, Capt Benjamin G. Patterson's Company; subsequently Co B, 23rd Regt Va Cav; organized 6/4/1863 and reported as such 3/7/1864 - assigned to 23rd Regt Va Cav per S.O. No. 99, A&IGO, dated 4/28/1864

41st Battalion, Virginia Cavalry (White's)
41st Cavalry Battalion was organized in September, 1863, with four companies, later increased to seven. This unit skirmished in western Virginia and the Shenandoah Valley, then in April, 1864, merged into the 23rd Regiment Virginia Cavalry. Lieutenant Colonel Robert White was in command.

23rd Regiment, Virginia Cavalry
23rd Cavalry Regiment was organized in April, 1864, by consolidating seven companies of the 41st Cavalry Battalion and two companies of O'Ferrall's Battalion. The unit served in Imboden's Brigade and was involved in various conflicts in the Shenandoah Valley. It disbanded during April, 1865. The field officers were Colonel Robert White, Lieutenant Colonel Charles T. O'Ferrall, and Major Fielding H. Calmese

I don't see him listed with the 23rd roster.