I believe it would be 3rd Virginia Cavalry, not WV!
Found this by Googling:
From U.S. Statutes at Large, Vol. 14, 39th Congress
CHAP. XXXVI. —An Act for the Relief of F. A. Patterson, late Captain of the Third Virginia Cavalry. — Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled. That the Secretary of War be, and he is hereby, authorized and directed to pay Captain F. A. Patterson full amount of pay and emoluments as a captain of the third Virginia cavalry from the twenty-__th day of November, eighteen hundred and sixty-two, the date of his commission by the governor of Virginia, to the date of muster out of his regiment. Approved, April 10, 1866
This had some weird letters and numerals in it - evidently did not transcribe to the format used.But you can Google the title and see the actual wording.It would not let me copy it, only this transcription.