I cannot locate these twins in the records. I would assume that having enlisted sometime in 1864, their service records did not make it to Richmond to survive in the archives. The last Companies A, B, & K muster rolls on record are for the bi-monthly period May/Jun, 1864. As such, we have no way of following those who enrolled thereafter.

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This information found through a Goggle search.

Hamilton County Confederates [Chattanooga, Tennessee]

DESHA, Hamilton 4GA Cav
Born in Richland District, SC June 30, 1848. Enl. 1864 with twin brother Hampton in Murray Co., GA. Baptist. Married (1933) in HC Edith Louise Royal King. Church of Christ. Died Oct. 1, 1935 at res. on Roanoke Ave. and buried CSA Cem. [NBFM2; TWP, 311; CT Oct. 2-3, 1935]

DESHA, Alexander Hampton 4GA Cav
Born in Richland District, SC June 30, 1848. Enl. 1864 in Murray Co., GA. Surr. Kingston GA, 1865. To Chatt. soon after. Baptist. Died Nov. 26, 1933 and buried CSA Cem. [CT Nov. 27, 1933]

http://www.chattanoogan.com/2005/8/16/70953/Hamilton-County-Confederates-D-F.aspx