From: Rabbi Akiva Eiger
To: Unknown recipient
An unmarried woman conceived illicitly, married a man who treated the child as his own, and the daughter sought to marry a Kohen. Rabbi Akiva Eiger rules the daughter is permitted even lechatchilah: since rejecting the mother's testimony would render the daughter a shesukis disqualified from the congregation, we must accept it fully (lo pelaginan diburah), which automatically renders her fit for kehunah; additionally, the pagum status of a gentile's child is at most rabbinic, and many poskim deny it entirely. Finally, since the husband himself affirms with certainty that the child is his, even Rabbi Yehoshua would permit the match, providing independent grounds to rule leniently lechatchilah.
Source: Shu"t Rabbi Akiva Eiger §91