Gemara

(Beraisa): If a Min (avid idolater) slaughters, the animal is an offering to idolatry;

Some say, his children are Mamzerim.

The first Tana holds that he does not allow his wife to have relations with others.

Sanhedrin 82a (Ravin): Beis Din of Chashmona'im decreed that one (a Kohen) who has Bi'ah with a Nochris is liable for Bi'ah with a Zonah;

Rav Dimi disagree, for Nochrim do not let their wives be like Hefker.

Yevamos 69a - Version #1 (Rav): If a Arus had Bi'ah with his Arusah (betrothed) in her father's house, the child is a Mamzer;

(Shmuel): The child is a Shtuki (i.e. of uncertain lineage).

(Rava): Rav discusses one suspected of Bi'ah with others. If not, we attribute the child to her husband.

Support (Mishnah): If (a Kohen raped or enticed) a Penuyah (single woman, and she) gave birth, she may eat Terumah.

If she were suspected of Bi'ah with others, she could not eat (perhaps the child is not from the Kohen)! Rather, she is not suspected of Bi'ah with others.

We attribute the child to him even when she is Asur to the Kohen like to all men (without Kidushin), and all the more so for an Arusah, who is permitted only to the Arus!

Objection (Abaye): Perhaps Rav disqualifies the child even when she is suspected only of him. She freely had Bi'ah with others, just like with her Arus. Our Mishnah discusses a woman locked in a jail cell only with a Kohen.

Version #2: Rav and Shmuel argue about a pregnant Arusah.

(Rava): Rav discusses when she is suspected of Bi'ah only with others, but not with her Arus. If she were suspected of Bi'ah also with him, we would attribute the child to him.

Support (Mishnah): If she gave birth, she may eat.

If she were suspected of Bi'ah only with him, the Mishnah would not need to teach that she eats! Rather, she is suspected also with others.

We attribute the child to him even when she is forbidden to all, and all the more so regarding an Arusah, who is permitted only to her Arus!

Objection (Abaye): Perhaps Rav disqualifies whenever she is suspected of others, even if she is also suspected of her Arus. In our Mishnah, she was not suspected of Bi'ah at all (except for the time she was raped or enticed).

Kesuvos 13b (Beraisa): A Penuyah who was secluded or became pregnant is believed (to say that the man was Kosher);

R. Yehoshua (to Chachamim): A woman who was taken captive is not believed to say that she was not defiled!

Chachamim: Here is different. There are no witnesses.

R. Yehoshua: Her pregnancy is like witnesses!

Chachamim: (We admit if she was pregnant, but not if she was only secluded. A captive is different, for) most Nochrim are immoral.

R. Yehoshua: (It is no different. When there is seclusion,) there is no guardian against Bi'ah.

Rishonim

Rambam (Hilchos Yibum 3:4): If one was Mezaneh (had extramarital relations) with a woman, whether she is single or married, and she became pregnant, and she admits that it is his son, he is considered his son for inheritance, but he is a Safek regarding Yibum. Just like she was Mezanah with him, she was Mezanah with others. How can he know that it is surely his son?! He has no Chazakah. It is a Safek. We are stringent. She does Chalitzah, but not Yibum.

Teshuvas ha'Rashba (610): Leah was serving Reuven in his house, and he sinned with her. She became pregnant. He was unsure if it was from him. He expelled her from his house. Later, he returned her, put her in his female relative's house at the time of the birth, and fed her and the baby. He was not at the Bris, due to shame or Safek if it is his son. Later he called the son his own, either because he believed that she was not with others, or because he resembled him. Reuven died with a wife, and without other children. Since he called him his son, he inherits him. Even if he is not really his son, he can give his property to him for a gift. Yibum is different. If an Arusah became pregnant, we rely on her to say that it is from her Arus, even if he denies it. This is like b'Di'eved. Regarding Yibum, she is not believed to exempt herself from Chalitzah. Would we believe her to exempt another man's wife (if she said that she is pregnant through him)? However, if we saw that she had Bi'ah with him, we establish the child to be his, even if she is suspected of Bi'ah with others. The Mishnah says that a Kohen who fathered a child through a Bas Yisrael permits her to eat Terumah. Since we saw the Bi'ah, we attribute the child to that Bi'ah. If we know that she had Bi'ah with another, it is a Safek who is the father, so she needs Chalitzah. If a woman gave birth, and nine months ago she was Shimon's wife, and seven months ago she was Levi's wife, this is considered a Safek.

Magid Mishneh: One who says 'this is my son' is believed to exempt his wife from Yibum (Bava Basra 134a). The Rambam holds that this is because he knows that it is his son. If he raped or enticed a woman, he is not sure that it is his son, so we are stringent. If she is married to another man, surely we can say that most Bi'os were with her husband, so perhaps the son is from her husband. If she is single, it depends on whether she is suspected of Bi'ah only with him, or also with others. If he is a Kohen, (the son and) she may eat Terumah (Yevamos 69a). In Version #1, this is only if she is not suspected of Bi'ah with anyone else. In Version #2, this is even if she is suspected of Bi'ah with others. The Rambam rules like Version #1 regarding Terumah, which is an Isur Torah. If so, also for Yibum we should believe him, especially according to Version #2! The Rashba says that if we saw the Bi'ah, we attribute the child to that Bi'ah, unless we know that she had Bi'ah with another. If she had different husbands nine and seven months before giving birth, it is considered a Safek. He holds like Version #2. Unless we know that she had Bi'ah with another, we assume that the first is the father. It is a Safek mid'Oraisa, so we should be stringent for both versions. If she is not suspected of Bi'ah with others, this is just like Terumah. Even if she is suspected of Bi'ah with others, perhaps the Halachah follows Version #2. Kesuvos 13b is like Version #2.

Teshuvas ha'Rashba (cited in Hagahos Maimoniyos, Hilchos Isurei Bi'ah 18:1): A Yisrael and his wife Hemiru (became Notzrim), and repented. How is she permitted to him? Surely, she is a Zonah. She intended for Zenus, for she wantonly permitted to herself all Aveiros. In Chulin, the first Tana holds that a Min does not allow his wife to have relations with others. Do not say that Nochrim are different, for no Nochri guards his wife. Rav Dimi holds that they do. Even Ravin forbids (due to Zonah) only due to a decree.

Note: What is the support from Ravin? Zenus forbids a woman to her husband. This does not depend on whether a Nochris is considered a Zonah!

Rashba (ibid.): It is proper not to forbid Ba'alei Teshuvah, for presumably they would not transgress a Torah Isur. A woman is forbidden only through warning and seclusion (Kesuvos 9a). Had she become a Mumar by herself and repented, we would forbid her, but there it is as if there are witnesses (of Zenus). If they both Hemiru, she is permitted, like R. Shimshon said.

Teshuvas ha'Rosh (82:1): A case occurred in which a Penuyah gave birth, and everyone said that Shmuel was the father. He agreed, and called the son like his relative's name. Shmuel did not attend the Bris. Perhaps he feared lest people say 'how do you know that it is your son? Perhaps she was Mezanah also with others!' A man is believed to say that 'this is my son from my wife' to exempt from Yibum. Here, he is not believed even through a Migo. This is like a Migo against witnesses, for almost surely, he himself is unsure. They were not locked together in a jail cell the entire time! Perhaps she was Mezanah with others! It just appears to him that it is his son. If a woman says 'there was a war, and I saw my husband die', the Gemara did not resolve whether she is believed. The Rif rules stringently. Perhaps she really saw, but she is not believed through a Migo, due to a Chazakah that she estimates. 'All these people are dying. Will he be spared?!' All the more so here he estimate, for he cannot know that it is his son. In Kesuvos we rule like R. Gamliel, who believes a Penuyah to say that her child is Kosher. This does not prove about or case. The Gemara says that a woman checks with whom she is Mezanah. Alternatively, we leave her on her Chezkas Kashrus (and say that she had Bi'ah with a Kosher man, therefore also her child is Kosher). These reasons do not apply here. Avi ha'Ezri rules like Version #2 in Yevamos, for only this version is brought in Kidushin 75a. Even if she is suspected of Bi'ah with others, we attribute the child to the Vadai Bi'ah. Surely we do so here, for she was designated for this man. I do not understand the Rambam. Since he says that the son is a Safek, why does he inherit him, and take money from Vadai heirs? Migo does not apply here. If you say that he is believed for inheritance Migo (since) he could give to him all his money, the same applies to Yibum, for he could divorce her to exempt her from Chalitzah! If he is believed about inheritance like R. Yehudah, who says that the Torah believes a father to say who is his firstborn, he should be believed also for Yibum!

Nimukei Yosef (Yevamos 23b DH Gemara): If a Penuyah gave birth and said that the baby is from Ploni, even though she is believed to say that the baby is Kosher, she is not believed regarding inheritance. This is even if she was a Pilegesh designated special for him.

Poskim

Shulchan Aruch (EH 156:9): If one was Mezaneh with a single or married woman, and she became pregnant, and he said that it is his son, even if she agrees, it is a Safek. She does Chalitzah, but not Yibum.

Rema: If a man and woman were locked together in a jail, if she became pregnant, surely it is from him, so the child exempts her from Yibum. Some say so even about a man who designated a harlot special for himself.

Beis Shmuel (15): Nowadays Terumah is mid'Rabanan. This is why the Rambam assumes that she did not have Bi'ah with others. The Bach asked why the Rambam is lenient about an Arusah, for this pertains to the Isur Torah of a Mamzer. I answer that also the Isur of a Safek Mamzer is mid'Rabanan. Perhaps he asked because everyone except for the Arus is Pasul to her, so the child should be considered a Vadai Mamzer. The Bach answered that since the Arus is permitted to her, we attribute the child to him. The Rambam says that if a Penuyah says that she is pregnant from a Mamzer, we are concerned lest she had Bi'ah (also) with others. This is difficult, for the Rambam holds that there is no Isur mid'Oraisa with a Shifchah! (Even if the child will marry a slave, even if he is a Kosher Yisrael, this is only an Isur mid'Rabanan, so we should be lenient - PF.) The Shulchan Aruch distinguishes between Torah and mid'Rabanan Isurim. Terumah is mid'Rabanan, and many Poskim hold that Shifchah is an Isur Torah. The Nimukei Yosef is concerned for Zenus even when she is designated for one man. The Rosh and Rashba are not concerned for a Safek Bi'ah with others if we know that she had Bi'ah with one man, even for Torah Isurim. The Magid Mishneh says so only when she is not suspected about others.

Gra (30): The latter opinion is the Rosh. This is even like Abaye according to Version #1. We learn from Kesuvos. Even R. Yehoshua says that the child is Kosher. R. Shimshon says that this is when she was constantly with him. We attribute most of the Bi'os to her husband. In Yevamos, he was with her only once. This entire Sa'if is like Abaye, in Version #1. However, the Rosh rules like Rava in Version #2, for Kidushin 75a is like him. The Rashba agrees. The Rambam rules like Abaye in Version #2.