There are several generations missing between your Patterson family in Florida and the Patterson family in Maryland. The obvious next step is to find the parents of your Alexander Patterson. Volunteers in the forum will profit by it if you can supply Alexander's birth date and place, spouse, places lived, census transcriptions, etc - anything you already know about him.
The Elizabeth Patterson (b abt 1785 in Baltimore) who married Jerome Bonaparte had brothers William Patterson b abt 1780 in Baltimore and Robert Patterson b 1783 in Baltimore - at least those are the brothers mentioned on this family tree. Your Patterson family could be descended from one of these brothers, or from a cousin of Elizabeth's - or via some other connection entirely.
Well worth looking into it. Sorry I don't have more for you.