Notice that William Verley is in the 1830 census of Manlius, Onondaga Co, NY. Also in the 1830 census of Manlius, Onondaga Co, NY is John Schermerhorn (age 50/59).
William Danford Verley and Hannah named their first child John Skimahorn Verley. I think that John Schermerhorn in the 1830 census is likely to be the father of Hannah.
My wife descends from John Schermerhorn b. abt 1800 -- I think he and Hannah are brothers.
I'm going to post a separate proposed lineage for them.