He may have been referring to McLain's 37th Mississippi Infantry, commanded by Colonel Robert McLain

However, I do not find him in any available roster of the 37th Mississippi, see, for one:

http://sheltonfamilyhistory.com/Documents/37th%20Regiment%20Mississippi%20Infantry.pdf

Company C -- Clarke County Rescuers (raised in Clarke County, MS)
http://www.mississippiscv.org/MS_Units/37th_MS_Inf.htm