Yibbum and Jewish brothers who share a Gentile father

Question

Suppose there are two brothers who share the same Jewish mother and non-Jewish father. One marries a Jewish woman but subsequently dies childless. Does yibbum/chalitzah apply in this situation, or are the widow and surviving brother exempt?

I have seen sources that say that both brothers must share the same father since yibbum relates to inheritance. In this case, they do share the same biological father, but this answer seems to imply that they are halachically unrelated.

EDIT: So ultimately the question boils down to this: Is it true in the context of Yibbum that brothers who share a non-Jewish father are not considered paternal brothers at all?

My hunch is that halacha may not be concerned with the inheritance or bloodline of the non-Jewish father. (On the other hand, maybe it depends on other factors, such as if the mother was in a Tzelofchad-like situation.) However, I have not yet found any sources that address this scenario. Sources would be greatly appreciated.

Answer 1

The Mishnah in Yevamos 97B states

הַגִּיּוֹרֶת שֶׁנִּתְגַּיְּירוּ בָּנֶיהָ עִמָּהּ לֹא — חוֹלְצִין וְלֹא מְיַיבְּמִין

Rashi explains that the reason is due to the fact that the non Jewish father does not count to make them family in Halacha:

דאחוה מן האב בעינן וגר אין לו שאר האב דרחמנא אפקרי' כזרע בהמה שנאמר (יחזקאל כ״ג:כ׳) וזרמת סוסים זרמתם

Later on he states further that yibum needs to be related through the father, and the non Jewish father is not counted:

דמידע ידעי דייבום מן האב הוא ועובד כוכבים אין לו אב

And again later he says the same idea:

לא חולצין ולא מייבמין - דצד ייבום מן האב הוא והני אין להם אב דזרע מצרי כבהמה

The Gemara on 97B on the bottom, brings a braisa that talks about twin brothers who were born to a giyores:

תָּא שְׁמַע: שְׁנֵי אַחִים תְּאוֹמִים גֵּרִים, וְכֵן מְשׁוּחְרָרִים — לֹא חוֹלְצִין וְלֹא מְיַיבְּמִין, וְאֵין חַיָּיבִין מִשּׁוּם אֵשֶׁת אָח. הָיְתָה הוֹרָתָן שֶׁלֹּא בִּקְדוּשָּׁה וְלֵידָתָן בִּקְדוּשָּׁה — לֹא חוֹלְצִין וְלֹא מְיַיבְּמִין, אֲבָל חַיָּיבִין מִשּׁוּם אֵשֶׁת אָח. הָיְתָה הוֹרָתָן וְלֵידָתָן בִּקְדוּשָּׁה — הֲרֵי הֵן כְּיִשְׂרְאֵלִים לְכׇל דִּבְרֵיהֶן. קָתָנֵי מִיהַת: אֵין חַיָּיבִין מִשּׁוּם אֵשֶׁת אָח, חִיּוּבָא לֵיכָּא —

The Gemara cites another proof. Come and hear: Two twin brothers who are converts, and similarly twin brothers who are freed slaves, do not perform ḥalitza for each other’s wives, and they do not perform levirate marriage with them, and if they engage in intercourse with them they are not liable to receive karet for engaging in intercourse with a brother’s wife. If they were not conceived in sanctity and only their birth was in sanctity, they do not perform ḥalitza or levirate marriage, but they are liable for engaging in intercourse with a brother’s wife. If they were conceived and born in sanctity, they are like Jews from birth in all of their matters. In any event, the baraita is teaching that regular converts are not liable for engaging in intercourse with a brother’s wife. It can be inferred that while there is no liability by Torah law

The Rambam Yibum 1:8 brings this as the Halacha.

While one may argue that this is specifically referring to children who convert, but if they were born after the mother’s conversion, perhaps, they would be able to do yibum. The Kiryas Sefer on that Rambam clarifies in this exact case that the Halacha is the same

ואפילו תאומים שנולדו בקדושה דגוי משעה שהזריע אפקריה רחמנא לזרעיה דכתיב וזרמת סוסים זרמתם וזרמת היינו זרע שהוא יורה כחץ כזרם מים המקלח בכח