There were 3 units that were designated as 3rd La. Cavalry. These regiments were commanded by Cols. Isaac Harrison, J. Frank Pargoud, and the other by James H. Wingfield. According to Booth, James Corkern was in Company A of Wingfield's Regiment. According to Arthur Bergeron's book, the 9th La. Battalion of Partisan Rangers were designated 3rd La. Cavalry in Sept, 1864. This unit participated mainly in eastern La. and S.W. Miss. They became part of Col. John S. Scott's Brigade (1st La. Cavalry in which 2 of my GG Grandfathers served in Co. H!!!). They fought minor skirmishes near Clinton, Bayou Sara, La. and Woodville and Liberty, Mississippi. Regiment surrendered at Gainesville, Al. on May 8, 1865. Company A, probably from Washington Parish was commanded by Capt. John Slocum. As the 9th Bat. Partisan Rangers, this unit organized at Camp Moore in May 1862. Fought as pickets at Port Hudson, the Battle of Baton Rouge, attempted to intercept Grierson's Raid, etc. For more info, see Bergeron's Guide to Louisiana Confederate Military Units, 1861-1865, pp.45-46, and 59-60. Hope this helps.
Kevin Templet, Graduate Student @ Southeastern Louisiana University.