Commentary for Kiddushin 136:5

Since the Jewish woman cannot have kiddushin with this man, because he is not Jewish, but she can have it with other men, if they are Jewish, this case should fit into the category of the mishnah that says the child of such a union is a mamzer. This would mean that the child of a non-Jewish man and a Jewish woman is a mamzer, and would not be allowed to marry an Israelite.
The Talmud rejects this—this child is not “fit” which means she cannot marry a Kohen. This is because there was a transgression in the union. But she/he is not considered a mamzer. She/he is Jewish and can marry an Israelite.