Mary Amanda Rumph Hestand filed Widow’s Pension Application, January 25, 1931, 29 years after Anthony’s death indicating he served in Company C, 31st Texas Cavalry, General Gano’s Brigade, S. H. Maxey’s Division. This appears to be the 1st Texas Cavalry, Arizona Brigade which was organized February 21, 1863, many of the men were first enlisted September 22, 1862 at Bonham, Texas.

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1st TX Cavalry Arizona Brigade
Organized: on 2/21/63 Mustered Out: 5/26/65

Regimental Assignments [partial]

April 1864 - July 1864
Gano's Brigade
Maxey's Cavalry Regiment
District of AR
Trans-Mississippi Department

Records for this unit are found in the National Archives Microfilm rolls:

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

Roll 195 Granbury’s Consolidated Brigade (1st Consolidated Regiment)
Hardman’s Cavalry (1st Regiment, Arizona Brigade: 31st Cavalry)
A - K

Roll 196
L - Z

Anthony Hestand is not recorded

These rolls may be found at Fold3 https://www.fold3.com

See below:

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These records show the officers of Company C

Company C, 1st Regiment Arizona Brigade, Hardman’s Regiment

J. H. Dameron, Capt.
Robt. R, Kerr, 1st Lt.
S. D. Robinson, 2nd Lt.
A. C. Kerr, 2nd Lt. [Enlisted Sept. 22, 1862 Bonham, Tex.]
H. J. McRea, 2nd Lt.

Rolls for most of these officers and a number of men were obtained from these rolls, but are not consistent for the enlisted men of the company:

Company Muster Roll September 22, 1862 to April 30, 1863
Company Return April, 1863
Company Return May 1863
Regimental Return July 1863, Camp Bankhead
Regimental Return March, 1865 Camp near Harrisburg
Regimental Roster May 11, 1865, Camp Kyle near Harrisburg, Texas

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The regiment was known at various times as the 1st Regiment Arizona Brigade, as the 31st Texas Cavalry and as Hardman’s Regiment Texas Cavalry

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