Depending on the time period, many different tribes were represented in northern
Alabama, including the Cherokee and the Creeks.
You will need to trace your family to, through and beyond your great-grandmother using the normal genelaogical methods (census, birth, death, marriage certificates, bible records, etc), and then try to tie those people through their names, both married and maiden names and family groups, to known tribal rolls. It is a slow process, but can be very rewarding.
I recommend you start with census records.
Carolyne