From records I have collected:
Mary Jay m. William Henry Schieffelin on 15 Oct 1863.
Mary was the daughter of John Jay (1817-1894) and
Eleanor Kingsland Field who were married on 23 Jun 1837 in Baltimore, MD.
John was the son of William Jay (1789-1858) and
Hannah Augusta McVicker who were married on 4 Sep 1812.
William was the son of Chief Justice John Jay and Sarah Van Brugh
I had not collected much on the female lines because I was identifying male
descendants for DNA testing. But my research indicates that your line is
that of the Chief Justice.