I'm almost certain that Grief Carroll, son of Daniel and Martha Carroll was an early settler in what became Madison County AL. Carrolls also ended up in adjacent counties of Limestone, Lauderdale and Lawrence. I believe Grief's sons, Jacob, James, Richmond and William are enumerated in the 1830 Census of Madison County. Grief Carrell is enumerated in the 1820 Alabama Census living in Limestone County. Grief (spelled Gruss Carroll in the Ancestry.com database) is on 1815 and 1816 tax rolls for Madison Co. There are recorded marriages between James and Rachel Edwards, and Richmond and Mildred McGee. This work is complicated by the existence of a Charles Carroll family apparently from SC in Madison CO at the same time.
Be aware that there is another Grief Carroll, son of Grief's son, William W.
If you are interested I have put together a spreadsheet of the descendants of Daniel Carroll in an attempt to keep straight who was whom and where they lived. If you're interested I'd be glad to share, but it's a work in progress certain to contain errors at this point.