I suspect this is his father:

Leroy C. Wright, age 42, Captain Kelly’s Company, 3rd Regiment Cavalry, Texas State Troops (6 Mos., 1863-4), enrolled January 30, 1864 at Netona by Captain J. T Brackenridge of men between the ages of 18 and 45, enrolled in compliance with G.O. No. 14, Jan. 20, 1864, at Houston, Texas, claims exemption under Stock Law, resident of Gonzales

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Leroy Wright, Private, Captain James M. Homsley’s Company, 1st Regiment Texas Mounted Riflemen,** enlisted September 30, 1861 at Camp Jackson by J. M. Homsley, value of horse $100, equipments $18,

his name appears on the Jan/Feb, 1862 muster roll not being recorded absent or present, no further records

Note, there are no further Company G muster rolls in the records

** This company was successively designated as Captain Frost’s Company and Captain Homsley’s Company, 1st Regiment Texas Mounted Riflemen, and Company G, 1st (McCulloch’s) Regiment Texas Cavalry. Re-organized May 28, 1862 forming part of the 8th (Taylor’s) Battalion Texas Cavalry

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Leroy Wright, age 18, Private, Company A, Taylor’s Battalion Texas Mounted Rifleman, enlisted September 30, 1861 at Camp Jackson by J. M. Hornsly, value of horse $140, equipments $25, furloughed for 60 days from June 25, 1862, on detached service from August 26, 1862, on detached service with horses from February 1, 1863, no further records

Note, there are no Company A muster rolls subsequent to that of March/April, 1863 which precludes knowledge of his later service

The 8th (Taylor’s) Battalion Texas Cavalry, or Mounted Rifles, was organized June 1, 1862, with five companies, four of which had previously served in the 1st IMcCulloch’s) Regiment Texas Cavalry.
The 3rd (Yager’s) Battalion Texas Cavalry, the 8th (Taylor’s) Battalion Texas Cavalry and Captain Ware’s Company Texas Cavalry were consolidated about May,1863, to form the 1st (Yager’s) Regiment Texas Cavalry

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Leroy Wright, 3rd Corporal, Company G, 1st (Yager’s) Regiment Texas Cavalry,* enlisted September 30, 1861 at Camp Jackson by Lt. Homsley for 3 years, recorded on the Jan/Feb, 1864 muster roll as absent, Prisoner, supposed to have been captured by the enemy while on picket duty over Matagorda peninsula [perhaps 12/28/29/1863] no further records

* Formed about May, 1863, this company was formerly Company A, 8th (Taylor’s) Battalion Texas Cavalry

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Leroy C. Wright, 1st Lieutenant, Benavides’ Regiment Texas Cavalry, recorded on the Return of Troops on the Line of the Rio Grande, Texas, September, 1864 as Absent, on duty with Company, no further records

M323: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Texas