The Rishonim (Medieval Halachic scholars) debate the question as to the status of a child produced by a Jewish mother and non-Jewish father. The Gemara in Masechet Yebamot (17) implies that according to the view of Rabina, a child’s status in such a case is determined by the mother’s status, but Tosafot in Masechet Kiddushin (75b) cites sources indicating that Rabina’s view is disputed. Different opinions exist among the Rishonim, but the Shulhan Aruch (Eben Ha’ezer 43) indicates that the status of such a child is determined based on the mother’s status. This is, of course, the accepted view. Therefore, the child of a Jewish woman is considered a Jew for all Halachic purposes, even if the father is not Jewish.

However, an interesting question arises in the case of a boy born on Shabbat to a Jewish mother and a non-Jewish father. Generally, when a boy is born on Shabbat, the Berit Mila is performed the following week on Shabbat. Although normally the infliction of a wound constitutes an act of Shabbat desecration, the Misva to circumcise a child on his eighth day overrides this prohibition. Rabbi Akiva Eiger (1761-1837) ruled (in Yoreh De’a, 255) that in the case of a child with a Jewish mother and non-Jewish father, the Berit Mila should not be performed on Shabbat. As mentioned, this child’s status is subject to a debate among the Rishonim, and although we follow the position that he is to be regarded as a Jew, Rabbi Akiva Eiger maintains that we must take into account the view that this child is not Jewish. And according to this view, circumcising the child on Shabbat is strictly forbidden, since there is obviously no Misva to circumcise non-Jewish children, and thus this Berit Mila does not override the Torah prohibition against inflicting a wound on Shabbat. Rabbi Akiva Eiger therefore asserted that in deference to this view among the Rishonim, the Berit Mila of such a child should be delayed until Sunday.

This view was also followed by the Maharam Shick (1807-1879), who reached this conclusion from a different angle. He notes that in an ordinary case of a baby boy born on Shabbat, when Shabbat starts the next Friday night, the infant has a "Hezkat Issur" – a de facto status of being forbidden for circumcision. Since Berit Mila may not be performed at night, the infant enters Shabbat on Friday night with a de facto presumption that circumcision is forbidden that Shabbat. The next morning, however, the Biblical requirement to circumcise on the eighth day changes this presumed status and makes circumcision permissible. In the case of a boy fathered by a gentile, however, the "Mi’ut" – the minority position among the Halachic authorities which considers this child a non-Jew – joins together with the initial "Hezkat Issur" to prevent the circumcision from becoming permissible. Therefore, the Berit must be delayed until Sunday.

This is also the view of Rav Yehonatan Eibshitz (1690-1764), in his work Ye’arot Debash (Derasha 1).

Others, however, disagree. Rav Eliyahu Halevi Shama (d. 1814), one of the great Rabbis of Aleppo, composed a colossal work on the laws of Berit Mila entitled "Machshireh Mila," which has become the official handbook, so-to-speak, for Sefaradim with respect to all laws and customs related to Berit Mila. In this work, he notes the Shulhan Aruch’s ruling that the newborn son of a Mumar – a Jew who abandoned the Jewish faith, Heaven forbid – who is born on Shabbat is given a Berit Mila the next Shabbat just like any other Jewish child. Rav Eliyahu Shama comments in this context that this applies as well to a Jewish child whose father is not Jewish – in direct contradistinction to the view cited above.

In practice, then, it would certainly be acceptable for Sefaradim to follow this ruling of the "Machshireh Mila" and perform the Berit on Shabbat in this case. It goes without saying, however, that given the different views that exist and the gravity of this issue, a competent Halachic authority should be consulted for guidance.

Summary: Although the child of a Jewish mother and non-Jewish father is considered Jewish in all respects, there is some question as to whether such a child who is born on Shabbat should be circumcised the next Shabbat, as an ordinary Jewish child would. It appears that Sephardic custom allows circumcising the child on Shabbat in such a case, though one should consult with a competent Halachic authority for guidance in this regard.