Some barred or disallowed Southern Claims were later appealed under the Bowman or Tucker Act. When appealed, the docket number for the appeal may be noted on a sheet of paper in the file folder for the original claim. 

Check the microfiche set, Barred and Disallowed Case Files of the Southern Claims Commission, 1871-1880 (M1407), available here in Special Collections, to see what a specific barred or disallowed file includes. If the paperwork for a claim consists only of a single document  containing the words "House of Representatives" printed on it, or possibly a notation such as "Rec'd sundry papers in above case" and signed by someone from the Court of Claims, then there is a good possibility that the claim was appealed. Check the five reel microfilm set, U.S. Court of Claims Docket Cards for Congressional Case Files, ca. 1884-1943, to see if there is a docket card for that person.

Keep in mind that Southern Claims were not the only type of claims brought before the U.S. Court of Claims. Therefore, finding a card or your person in the docket index cards does not guarantee that the case involved an appealed Southern Claim. An index card could reference some other type of claim that may also be of interest.