I'm looking for information on my great-great-grandfather William Wallace Garner. I believe he served during the Civil War. The National Parks web service shows a William W Garner serving with this unit. However there are several other William Garners (no middle initial) listed as well in various units. How can I verify which, if any, are him?

This what I know about him:

William Wallace Garner
born c. 1830
died c. 1880-1910 (alive on 1880 census, wife is living with son George on 1910 census)
lived and died in Carroll County, MS. Should be buried out at Pine Bluff. Not sure if there is a marker.
Wife's name was Mathilda Catherine (?)

This is what I believe about his service:

Rank:Private
Unit: 1st MS Light Artillery, Company C (Turner's Battery)

Had a brother-in-law W.D. (William Daniel) Herring that also served in this unit. I don't think any other relatives served, but I could be wrong.

I don't know if his wife filed for a pension.

What other information can you give me regarding this unit? What were some of the major battles where they fought? How do I go about getting copies of his service records?

Thanks.