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Actually, I have David Jacox as b. ca. 1775, but no notion of who his parents were. If he was b. ca, 1755, then he was not the David, son of Francis of Poughkeepsie. There were cousins? brothers? uncles? of Francis who apparently moved to Philipstown, NY in the early 1700's from Hempstead. Francis of Poughkeepsie is generally held to be the same Francis in the 1698 census of Hempstead, son of David and Hannah Jaycocks. David was the son of William, son of Francis and Grace Jeacockes. David had a brother, Benjamin, who is said to have been in Fishkill about 1737-40. Benjamin married Jannetje Jones 1JUL1741, and they may have had a son, Benjamin. It is believed that Benjamin started the Philipstown family, but nothing is really clear on that point.
The name, David, was very popular with the Jaycocks, especially (perhaps only) with those descended David in Hempstead. Francis of Poughkeepsie may have had a brother, David, and another brother was Joseph Jaycocks, who was in the Southern Precinct of Dutchess Co. (now that part of Dutchess Co. which was split off to make Putnam Co.) by 1744. The best that I can offer is that your David was most likely descended from David of Hempstead. Not enough work has been done on the Westchester/Putnam/Dutchess Counties families to be able to sort them out. I would also suggest that you try corresponding with Sharilyn Whittaker, whom you will find on this forum, as she is probably the most conversant with the difficulties you are encountering.