Safek Mamzer cannot marry
A Safek Mamzer can marry a giyores, just as can a certain mamzer.
Where do you know that from? (This is a request for information, not a challenge.)
Good question. I can’t point to a specific source off the top of my head (and I don’t have the time to do research now). However, there is a logical reason to say so:
If a kohen marries a gerusha (who is certainly less of an issur than a mamzeres, as the former is permitted to all other Jews) the offspring has no kohanic status. Certainly then, if he married a woman who is forbidden to all natural-born Jews, certainly the offspring loses kohanic status.
I’ll see if I can find an explicit source over Shabbos.
The Wolf