Kesubos Chapter 1, Mishnah 9. This mishnah is understood almost exactly like the previous one, but while the previous mishnah dealt with the woman's own fitness to marry, here the discussion turns to the fitness of the fetus - the child conceived from relations with a man whose identity we do not know.
The words of the mishnah:
"Haysah me'uberes, ve'amru lah: mah tivo shel ubar zeh?" - the woman was pregnant, and they asked her about the nature of the child not yet born, that is: who is the father?
"Me'ish peloni ve'kohen hu" - this is her answer. She does not necessarily mean a kohen specifically; the point is that the father is a Jew of unblemished lineage, and therefore the child is fit as well.
The Tanna'im disagree about this:
"Rabbi Eliezer omer: ne'emenes" - the woman stands in a presumption of fitness, and consequently the child too stands in a presumption of fitness. If a daughter is born, she is fit to marry a kohen.
"Rabbi Yehoshua omer: lo mipiha anu chayin" - we do not rely on her word, and she is not believed to say that she had relations with a Jew of unblemished lineage. Therefore we must adopt the stricter possibility: "Harei zu bechezkas me'uberes lenasin ulemamzer, ad shetavi re'ayah lidvareha" - we assume that she is pregnant from a nasin or from a mamzer, until she brings proof that the child is from a man of unblemished lineage.
It emerges that according to Rabbi Yehoshua both of them are disqualified - the mother and also the daughter born to her - and neither may marry a kohen.
In summary: this mishnah discusses the fitness of the child, as a direct continuation of the previous mishnah's discussion of the mother's fitness. According to Rabbi Eliezer the woman is believed by virtue of the presumption of fitness, and the child too is presumed fit; according to Rabbi Yehoshua we do not follow her word, and the child is presumed to be from a nasin or a mamzer until she brings proof for her claim.