In Pelletreau's "Early Wills of Westchester County, NY 1664-1784 there is a brief abstract of the will of Jeremias Canniff.
"Jeremias Caniff, Phillipsburgh, leaves to son Richard "the frm where I now live", and Richard is to pay John Shute L10.Rest to sons John, Jonas, James, daughters Ann Shute and Elizabeth Hunt."
Written11 May 1763 Probated 28 May 1764
So this documents the connection of Richard to Jeremias and Antje de Rivier, and I have a lot on his line and that of his parents Jeremias and Ann Woelffs. And, there was evidently a Jeremias Akenif before these in the picture, about which I have a little as well.
Let me ruminate on the implications of what you have written and get back to you.