Here's the only J. J. Price I could find

J. J. Price, Private, Capt. Truss' Company of Barbiere's Battalion of Cavalry, enlisted September 24, 1863 at Elyton, Ala. by Capt. Gantt for the duration of the war, last recorded present at the end of the year 1863 muster, no further records

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E. O. Price, Private, Capt. Truss' Company of Barbiere's Battalion of Cavalry, enlisted October 12, 1863 at Elyton, Ala. by Capt. Gantt for the duration of the war, last recorded present at the end of the year 1863 muster, no further records

Barbiere's Battalion Alabama Cavalry appears to have been formed of independent companies which had been organized for local defense and were serving with the Alabama Reserves

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BARBIERE'S RESERVE CAVALRY
Mustered Out: 5/4/65 at Citronelle, AL

Barbiere's reserve cavalry consisted of six companies under the
command of Maj. Joseph Barbiere, and served principally in
central Alabama during the fall and winter.
Source: Confederate Military History, vol. VIII, p. 303

Thomas K. Truss, Capt. Supporting Forces to Bureau of Conscription
Signs a Voucher for forage for 84 horses March 8, 1864 at Talladega, Ala.
Signs a Voucher for forage for 60 horses for the month of May 1864 at Elyton, Ala.
Signs a Voucher for forage for 32 horses for the month of June 1864 at Elyton, Ala.
Signs a Voucher for forage for 86 horses October 25, 1864 at Talladege, Ala.
Signs a Voucher for forage for 96 horses 13 February 1866 [sic] at Talladege, Ala.