The Headquarters element for the New York Army National Guard is known as “JFHQ” or, more officially, "Joint Force Headquarters." It shares its patch and "distinctive unit insignia" with he 53rd Troop Command, which is technically aligned as a separate "Major Command."

Joint Force Headquarters Patch

The shape of the patch is the same as that of First Army, the command area of which New York is a part of.
The blue background is the State Color.
The yellow crown is from the Statue of Liberty in New York Harbor, long a symbol for New York.
The vertical Red Sword is both a symbol and a color representing Command.