Gemara

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

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

(Rava): Presumably, Rav's law when we (have grounds to) suspect her of Bi'ah with others. If not, we attribute the child to her husband.

Support (Rava, for himself - Mishnah): If she gave birth, she may eat.

Suggestion: We do not suspect her of Bi'ah with anyone else. Even though she is forbidden (mid'Rabanan) to the Kohen and to all men (without Kidushin), we assume that the child is from him. Here, an Arusah is permitted to her husband and forbidden to all others. All the more so we should assume the child is from her husband!

Objection (Abaye): Perhaps Rav disqualifies the child even when we suspect her only of him, and not of others. We say, just like she freely had Bi'ah with her Arus, she freely had Bi'ah with others. Our Mishnah discusses when she was locked in a jail cell with the Kohen.

Version #2: If we know that the Arus had Bi'ah with his Arusah, Rav and Shmuel agree that we attribute the child to him. They argue about a pregnant Arusah.

(Rav): The child is a Mamzer.

(Shmuel): The child is a Shtuki.

(Rava): Presumably, Rav's law is when we do not suspect her of Bi'ah with her Arus, and we suspect her of Bi'ah with others. If we suspected her of Bi'ah with him, even if we also suspected her of Bi'ah with others, we would attribute the child to her husband.

Support (Rava, for himself - Mishnah): If she gave birth, she may eat.

Suggestion: We suspect her of Bi'ah also with others. Even though she is forbidden both to him and to all others, we assume that the child is from him. Here, an Arusah is permitted to her husband and forbidden to all others. All the more so, we should assume that the child is from her husband!

Objection (Abaye): Perhaps Rav disqualifies the child whenever we suspect her of others, even if we also suspect her of her Arus. In our Mishnah, we do not suspect her of Bi'ah at all.

Kesuvos 13b: An Arus and his Arusah came in front of Rav Yosef. Both said that she is pregnant from him.

(Rav Yosef): There is no reason to be concerned. Firstly, the husband admits. Also, Shmuel taught that the Halachah follows R. Gamliel (regarding a single girl)!

Question (Abaye): Your connote that it suffices that the Halachah follows R. Gamliel, even when the husband does not admit. But Shmuel told Rav Yehudah not to be lenient like R. Gamliel unless most people in the area do not disqualify her. Here, everyone except for the husband disqualifies her!

Answer (Rav Yosef): If the Halachah follows R. Gamliel, why did Shmuel require a Kosher majority? You must say that the Halachah follows R. Gamliel b'Di'eved. L'Chatchilah, we require a Kosher majority. Also our case is like b'Di'eved!

Kidushin 69a (Mishnah): Ten different lineages came up with Ezra from Bavel - ... Shtuki (one who knows his mother but not his father)...

Aba Sha'ul calls a Shtuki 'Beduki' (one who was checked).

74a: This means that we ask his mother. If she says that his father is Kosher, she is believed.

(Rava): The Halachah follows Aba Sha'ul.

(Mishnah - R. Elazar): Doubtful Mamzerim, i.e. Shtuki, Asufi and Kusi, may not marry definite nor doubtful Mamzerim.

(Rav Yehudah citing Rav): The Halachah follows R. Elazar.

Shmuel: Hillel taught that 10 lineages came up from Bavel, and all can intermarry How can you say that the Halachah follows R. Elazar?!

Contradiction (in both Rav and Shmuel): If an Arusah became pregnant, Rav says that the child is a Mamzer and Shmuel says that he is a Shetuki;

Rav says, the child is a Mamzer, and is permitted to a Mamzeres;

Shmuel says, he is a Shetuki, and is forbidden to a Mamzeres.

Answer #1: We must switch the opinions. Rav says, the child is a Shetuki. Shmuel says, he is a Mamzer.

Answer #2: Do not switch the opinions. Rav did not call the child is a Mamzer to permit him to a Mamzeres, rather, to forbid him to a Bas Yisrael;

Answer #2A: Rather, Shmuel holds that we Mashtik (silence) him from inheriting his father. Even if he took the money, we make him return it.

Answer #2B: Rather, Shmuel said he is a Shetuki, i.e. a Beduki. We ask his mother; she is believed to say that he is Kosher.

Shmuel already said that the Halachah follows R. Gamliel regarding a single girl. Here he teaches that even a married woman is believed, even though most men are forbidden to her.

Rishonim

Rif (Yevamos 23b): If an Arus had Bi'ah with his Arusah in her father's house, Rav says that the child is a Mamzer, and Shmuel says that he is a Shtuki.

Rosh (Yevamos 7:7): In the first version in Kidushin Rav holds that the child is a Vadai Mamzer and is permitted to a Mamzeres, for he holds that Safek Mamzerim may marry Vadai Mamzerim. Shmuel holds that the child is a Shtuki and is forbidden to a Mamzeres, for he forbids Safek Mamzerim to Vadai Mamzerim. We needed to switch the opinions because Rav rules like R. Elazar who forbids Safek Mamzerim to Vadai Mamzerim, and Shmuel rules like Hillel who permits. In another version, we say that Rav meant that the child is a Safek Mamzer, and is forbidden to a Mamzeres. Shmuel called the child a Shetuki, i.e. we silence him from inheriting his father, even if he seized the property. Rav and Shmuel taught different laws; they do not argue. This is if we did not ask his mother. If we did, she is believed to say that he is from the Arus and is Kosher. In Kesuvos (14a) Shmuel rules like R. Gamliel, and it is clear there that this is the Halachah. In a third version Shmuel calls the child a Beduki, for we ask his mother and she is believed. In this version Rav disagrees and does not believe his mother. We hold like Shmuel, for Rava rules like Aba Sha'ul.

Rif and Rosh: Some say that if an Arus (Vadai) had Bi'ah with his Arusah, Rav and Shmuel agree that we attribute the child to him. They argue about a pregnant Arusah. Rav says that the child is a Mamzer, and Shmuel says that he is a Shtuki. In Kidushin, we conclude that Rav calls the child a Safek Mamzer, and forbids him to a Mamzeres. Shmuel called the child a Shetuki, i.e. a Beduki. We believe his mother to say that he is from the Arus and is Kosher. The Halachah follows Shmuel, for he holds like Aba Sha'ul, who calls a Shetuki a Beduki, even when most men are forbidden to her. Rava rules like Aba Sha'ul. Surely, Shmuel agrees that the child is a Safek Mamzer if she does not know who the father is.

Nimukei Yosef (DH Gemara): Rav says that the child is a Mamzer. The child of a Nesu'ah is Kosher even if she is suspected of others, because most Bi'os are with her husband. An Arus is different, for he does not normally have many Bi'os before Chupah. In the second version Rav agrees when there are witnesses of even one Bi'ah, or when the Arus admits. They argue about when there are no witnesses and the Arus does not admit, is not here, is silent or does not remember.

Rambam (Hilchos Isurei Bi'ah 15:17): If an Arusah became pregnant in her father's house, the Chazakah is that the child is a Mamzer. He is forbidden to a Bas Yisrael and also to a Mamzeres. If we asked his mother; she is believed to say that he is from the Arus and is Kosher.

Rambam (18): If there were rumors that she was Mezanah with her Arus and had Bi'ah with others, even if the Arus (Vadai) had Bi'ah with her, the child is a Safek Mamzer. Just like she freely had Bi'ah with her Arus, she freely had Bi'ah with others. If we asked her and she said that she had Bi'ah (only) with her Arus, the child is Kosher.

Magid Mishneh: The Rambam holds that we always consider the child to be a Safek Mamzer before we ask her unless we know that the Arus had Bi'ah with her and there are no rumors that she was Mezanah with others. This is like Version #1 in Yevamos. Even though the Halachah follows Shmuel, Shmuel is Machshir only after she is checked.

Poskim

Shulchan Aruch (4:27): If an Arusah became pregnant in her father's house and she says that she is pregnant from the Arus and the Arus agrees or is not here, the child is Kosher.

Taz (15): If the Arus died, l'Chatchilah she or the child may not marry a Kohen unless the Arus agreed that the child is from him.

Shulchan Aruch (28): If there were rumors that she was Mezanah with her Arus and with others, even if the Arus (Vadai) had Bi'ah with her, the child is a Safek Mamzer. Just like she freely had Bi'ah with her Arus, she freely had Bi'ah with others. If we asked her and she said that she had Bi'ah (only) with her Arus, the child is Kosher.

Gra (71): The text should say '...rumors that she was Mezanah with her Arus or with others. In either case the child is a Safek Mamzer until she says that he is Kosher.

Chelkas Mechokek (29): The Magid Mishneh (Isurei Bi'ah 15:18) says that the Rambam rules like the first version. However, in Hilchos Yibum (3:4) he prefers the second version, and do does the Rosh (Teshuvah 82:1).

Beis Shmuel (48): The Rosh and Rashba rule like the second version only if we know that the Arus had Bi'ah with her. Here, 'rumors' means that we are almost sure that there was Bi'ah.

Rema: The same applies if she had Bi'ah with her Arus and there are no rumors that she was Mezanah with others.