There is reasonable info here
https://ancestors.familysearch.org/en/LZPJ-M53/barbara-ann-potter-1807-1873 which is helpful. Looks as though Thomas joined the army in 1793, was injured in Egypt in 1801 and posted back to Nottingham where he married Mary Shaw in 1802. Then to Jersey where 3 children were baptised, left the army in 1811, 2 children bpt in Ilkeston, moved to Nottingham St Mary where several more children were bpt and buried. According to 1841 and 1851 census and father's occupation on Barbara's second marriage certificate Thomas was a blacksmith. Thomas died in 1853 quickly followed by Mary - Nottingham Journal 4/3/1853 "On Sunday last, aged 80, Mary Potter, Orchard's-yard, Butcher Street, Nottingham, having survived her husband (Thomas Putter) only seven weeks"
My best guess is that Mary's place of birth from the 1851 census is Carlton which is in the parish of Gedling and very convenient for Nottingham St Mary's. I can't get a handle on where the Gedling parish registers circa 1773 are. I can find a James Shaw on the 1851 census who says he was born in Carlton in 1779 but cannot find anything for Carlton/Gedling online around that time.