Joshua Jr and Frances Pettijohn had a son George, just not the one that was connected. His son George was born about 1785 and we know of him because he testified in an 1837 trial involving his father: https://www.ancestry.com/mediaui-viewer/collection/1030/tree/661200...
George Perkins who had been connected to Joshua Jr and Frances, is the son of Isaac Perkins Jr and Hannah Sweat.
Sorry Erica Howton for creating so much work for you! <3