Apparently, your Alonzo Kerlin's father was a William J. Kerlin. Here is some service information for him.
Name: William J Kerlin ,
Residence: Spalding County, Georgia
Enlistment Date: 12 Aug 1862
Enlisted as a Private on 12 August 1862
Enlisted in Company I, 13th Infantry Regiment Georgia on 12 August 1862.
Wounded on 27 September 1864 at New Market, VA
Died of wounds Company I, 13th Infantry Regiment Georgia on 01 October 1864
If you'd like to obtain his Compiled Military Service Record and search for a pension file, you can do so by clicking on the link below.