Yevamos 42a: Rava said: The reason why a woman must wait three months after her divorce to get remarried is because she might have a baby and we won’t know who the father is, and the baby might end up marrying his sister from his father’s side.
יבמות מב ע”א: רבא אמר: גזירה שמא ישא את אחותו מאביו.
The Taz in Yoreh Deah 195:7 brings that Rabbeinu Peretz was once asked: why is a Jewish woman particular not to sleep on another man’s sheets, out of fear that she might get pregnant from that man’s sperm, but she has no problem sleeping on her husband’s sheets when she is a niddah? (Based on the Pischei Teshuva 195:8, this would be permitted only when the sheets were not specifically designated for the husband, or when the husband is not present.) If she gets pregnant from her husband’s sperm, wouldn’t the child have the spiritual disadvantage of being a “ben niddah”? Rabbeinu Peretz replied that since the child was not born from a forbidden sexual act, he is not a “ben niddah,” and even if he were born from another man’s sperm, he would not be a mamzer. The real reason to avoid another man’s sheets is so that the child knows who his father is, so that he doesn’t end up marrying his sister.
This problem is relevant today when couples do artificial insemination from a sperm donor. By law, the sperm donor’s identity has to remain confidential. Rabbi Yisroel Reisman once had a bochur in his yeshiva who knew that he was conceived from a Jewish sperm donor. Rabbi Reisman was not able to obtain his name, but he got the month and year when the donor was born. He and his beis din wrote a letter for the bochur saying that he could marry any girl, provided that her father was not born in that month.
Source: Shiur by Rabbi Reisman, Yoreh Deah 195
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