No birth certificate, no matter how cleverly forged, changes the fact that his father was never a citizen of the United States.
Well, yes, unless the birth certificate says that, in fact, his father WAS a citizen of the U.S.
Depends entirely on who his father actually was.
List only those facts that you know about Barry0 — provable facts, not speculation and not the “official” bio or book.
You can do it on a Post-It note.