IsStatenIsland
What's wrong with it?

That's correct for Ellis island.

NY and NJ agreed on the interstate boundary in the Hudson and Ellis Island, as it was at the time as shown by the current border, was agreed to be part of New York. In the mean time, the federal government had a fort on the island and it eventually turned into an immigration entry point. The federal government expanded the island between 1890 and 1934.

New Jersey sued New York in 1998 over NY claiming to own all the land that was built in NJ waters. The SCOTUS ruled in favor of NJ thus resulting in New York's small exclave within the island.