If your Cay family is from Puerto Rico, I know that my ancestors came from the Dominican Republic from Tulon France in circa 1700's. They were French Huegonat Sailors, I don't know that they were French or that they just lived there, and landed in the Dominican Republic. Then they went to Cuba, and then to The USA.
So we may have a connection there.
I am Phillip Cay, My father was Raymond Cay, his father was John Presley Cay, and JP Cay's father was Henry F. Cay.
I hope we can find a connection.
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I have been doing research for about 20 years.