It looks like the father of Susannah Rider was named Adam Curry. FamilySearch believes that it's this guy: Capt. Adam Curry
From https://www.vagenweb.org/bath/bird-4.htm "1796 - John RIDER (1773-1855) married first, 12 Feb 1796, in Rockingham Co., Va., to Susanna CURRY, dau. of Adam CURRY; Jno. WALSH, bondsman. John RIDER's name is recorded as "John RADER" in the marriage record. She died 4 Oct 1834, at Springston, Harrison Co., Va. and he married second to Susannah STOUT. He died, 1855. in Barbour Co., WV. See Rider, Fremont RIDER/RYDER GENEALOGY (1858)"
So far I have not found an original document to verify her father's name; but page 101 of the digital book at https://www.familysearch.org/search/catalog/1157962?availability=Fa... shows that Jno Walsh was the bondsman, so the claim looks accurate. Additional evidence: Susannah's FamilySearch profile at https://www.familysearch.org/tree/person/details/L87Y-WTQ shows that she has a well-documented son named Adam Curry Rider.
Overall it looks like the family of John Rider, Sr. alternated pretty freely between Rader and Rider, and Reider might be an alternate spelling. John has a couple of alter egos on Wikitree: https://www.wikitree.com/wiki/Rader-22 and https://www.wikitree.com/wiki/Rider-4
The children of John and Susannah don't appear to be well documented, and I'm not convinced that they are the parents of Hannah Vance It's possible, but I haven't seen any documentation.
