I have done minimal research on the Andertons of Bedford County, TN in an attempt to trace the families of some Anderton cousin-in-laws (wife's cousins). I haven't been able to get back to a settler from out of state prior to the early 1800s, but would be very happy to share my file if you are interested and will contact me directly. I did find a brief reference below to a Peter Anderton. Could this be your ancestor?
The full regimental history and roster of men can be found at http://www.angelfire.com/ego/37tninf/tnhistoryhttp://www.angelfire.com/ego/37tninf/tnhistory. Anderton family ancestors James Martin Byrom (listed here), J.W. Anderton and William Melvin Ray were all three members of Company A who were known as “Thompson Creek Grays”.
I found a roster of A Company: http://www.angelfire.com/ego/37tninf/Acompany.htmlhttp://www.angelfire.com/ego/37tninf/Acompany.html.Guys with Anderton, Ray and Byrom surnames were found as follows: 1st Lt. Milton S. Ray; Corporal George H. Ray; Privates James W. Anderton; John W. Anderton; Peter J. Anderton; William H. Anderton; James M. Byrom; John Byrom; Milton Byrom; Richmond D. Byrom (with note: died Sep 25 1864); Hezekiah Ray; Joseph S. Ray; Thomas C. Ray; and William G.M. Ray. Since all these folks were neighbors in civilian life, they were mostlikely otherwise related. – LDC 2003