Kiddushin 68B

ולדה כמותה מנלן? דאמר קרא: ״האשה וילדיה תהיה לאדניה״.

from where do we derive that her offspring is like her? The Talmud answers: As the verse states with regard to a Hebrew slave who marries a Canaanite female slave: “The wife and her children should be her master’s” (Exodus 21:4). This indicates that the offspring of a Canaanite female slave and a Hebrew slave are slaves, as she is.

נכרית מנלן? אמר קרא: ״לא תתחתן בם״. אשכחנא דלא תפסי בה קידושי, ולדה כמותה מנלן?

§ The Talmud asks: From where do we derive that betrothal with a non-Jew woman is ineffective? The verse states: “Neither should you make marriages with them” (Deuteronomy 7:3), which teaches that marrying non-Jew women is halakhically meaningless. The Talmud asks: We have found that betrothal is ineffective with her; from where do we derive that her offspring is like her?

אמר רבי יוחנן משום רבי שמעון בן יוחי: דאמר קרא: ״כי יסיר את בנך מאחרי״⁠ – בנך הבא מישראלית קרוי בנך, ואין בנך הבא מן הנכרית קרוי בנך, אלא בנה.

R' Yoḥanan says in the name of R' Shimon ben Yoḥai: As the verse states with regard to the same issue: “Your daughter you should not give to his son…for he will turn away your son from following Me” (Deuteronomy 7:3–4). Since the verse is concerned that after one’s daughter marries a non-Jew, the father will lead his children away from the service of God, this indicates that your son, i.e., your grandson, from a Jewish woman is called “your son” by the Torah, but your son from a non-Jew woman is not called your son, but her son.

אמר רבינא: שמע מינה: בן בתך הבא מן הנכרי ⁠– קרוי בנך. נימא קסבר רבינא נכרי ועבד הבא על בת ישראל ⁠– הולד ממזר?

Ravina said: Learn from it that the son of your daughter, born to a non-Jew, is called your son in all regards. The Talmud asks: should we say that Ravina holds that with regard to a non-Jew or a Canaanite slave who had sex with a Jewish woman, the offspring is a mamzer? One can infer from the fact that the offspring of this union is called “your son” that he is a Jew, and therefore the principle stated in the Mishnah should apply: If a woman cannot join in betrothal with someone, their child is a mamzer.