What I have on this Jonathan is the following (index codes and all):
6JDEAD. .i.Cornell: Jonathan; Cornell, son of .i.Cornell: Joseph
(Jr.);Cornell (Jr.) and wife .i.Hadden: Sarah; Hadden, was born in
1764 and died in 1834. He married (1) .i.Carpenter: Lydia; Carpenter
(dau. .i.Carpenter: Caleb; Carpenter) and (2) .i.Acker: Jemima; Acker
(no dates). CG names 7 children without indicating which wife bore
whom (Seems likely at least four were by 1st, since "Zeno" was a
Carpenter name.): , ,
7JDEADA. .i.Cornell: Caleb;, b. 1790, m. .i.Lamoree: Phebe; Lamoree
7JDEADB. .i.Cornell: Joseph;, b. 1793, m. .i.Merritt: Deborah D.; Merritt
7JDEADC. .i.Cornell: Zeno;, b. 1795, d. 1795
7JDEADD. .i.Cornell: Zeno;, b. 1796, m. .i.Brown: Mary; Brown
7JDEADE. .i.Cornell: Philip Ward; (no further record)
7JDEADF. .i.Cornell: Deborah; (no further record)
7JDEADG. .i.Cornell: Sarah D.;, m. .i.Carpenter: Isaac L.; Carpenter
This is partly attributable to Prentiss Glazier, but the family also
appears in the 1902 Cornell Genealogy as well as Doherty (Dutchess
Co.) and Bolton (Westchester Co.). Some people decline to put much
faith in Glazier, but I have the two other sources in this case, too.
None say that Jonathan was the son of Willett.
If there is good evidence of Jonathan being connected to Willett, I'd
like to see it.