While I do not have any info on Civil War service, I do have information on a J N Williamson buried in Attala County.

J. N. Williamson
born 22 Oct 1847
died 28 Sep 1909
age 61,
buried in Yockanookany Bap Cem., Attala Co, MS.

Is he your John Newton? If yes, can you provide details on his parents and siblings. Thanks.