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The suffix "Jr." was widely used in the 18th and early 18th centuries to denote that there was another, elder person by that name in the county - - - and there was an older Joseph Fulford in 1796, but not the father of the Joseph who married your Charlotte Ann Fulford.
I know of two other Charlotte Ann Fulfords. Clifford and Alice Fulford had a Charlotte Ann, b. 1805 born in Carteret Co, NC, who married John Nelson Bishop in Carteret. They moved to Marengo Co., AL. William and Abigail Fulford of Carteret Co. had a daughter, Charlotte Ann, b January 08, 1838, in Marengo Co. Philip Stephen Fulford and Charlotte Fulford of Carteret Co. had a daughter Clarky Ann, who was b. after 1825 in Marengo Co.
I have Stephen Fulford and Mary Davis, parents of your Charlotte Ann (b. ca. 1771), also with a daughter named Clarky, b. ca. 1778-1780, who married a Philip Fulford. I'm not sure where this came from, I have doubts about it.