Kiddushin 4:7

Rabbi Eliezer ben Yaakov says that if a Yisroel marries a female convert, his daughter may marry a kohein; if a convert marries a girl from a Yisroel family, his daughter may marry a kohein; if a male convert marries a female convert, his daughter may not marry a kohein. Whether a convert or a freed servant, their daughters may not marry kohanim until there is a mother in the line from a Yisroel family. Rabbi Yosi says that if a male convert marries a female convert, his daughter may marry a kohein.

Kiddushin 4:8

If a man says that his son is a mamzer, he is not believed. Even if both parents say that the fetus in her womb is a mamzer, they are not believed. Rabbi Yehuda says that (in both cases) they are believed.