http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=14809985

This the website for the grave of Joseph.S. (Simpson) Parrish, the caption says Co "C" 15 th Alabama infantry which in fact mthe headstone is marked Co "G". There is no Joseph Parrish in company C or company "G", but being that he disappeared in January of 1864, with the history of anguish the civil war caused , I would not be surprised if in fact he changed his name & age because he planned on disappearing anyway.

He was born in Lowndes Cty,Ala. had a brother die in Chapel Hill,TX and Joseph is buried in Silsbee, TX along with one son James T. Parrish and wife Gertrude (Adams) Parrish.
This is just my guess, I could be wrong if I could find a Joseph Parrish in another company of 15th.