The Torah commands to perform a Brit Mila on the eighth day after birth, even if it falls on Shabbat. Nevertheless, the misva of Brit only supersedes the prohibition of violating Shabbat when performed in its proper time. If the Brit was postponed for medical reasons, or in the case of a convert, it is forbidden to perform the Brit on Shabbat.
The Rashbes (Rav Shimon ben Semach Duran, Algiers, 1361-1444) adds that a postponed Brit cannot be performed on a Thursday. Since the third day, which is the most painful and dangerous for the baby, will fall on Shabbat, one is not allowed to create, in advance, a situation in which it will be necessary to violate Shabbat for the sake of the baby. This position is quoted by the Bet Yosef (Siman 248) and by the Hida(Rav Haim Yosef David Azulai, 1724-1807).

Hacham Ovadia in Yabia Omer cites the Korban Netanel (Rav Netanel Weil, Germany, 1687-1769) that the restriction on performing a postponed Brit three days before Shabbat, does not apply to Yom Tob. If, for example, Yom Tob fell on a Wednesday, it would be permitted to perform such a Brit on Monday.

Moreover, The Hida quotes the Taz (Rabbi David Segal, Poland, 1586-1667 in Siman 248) who prohibits performing a postponed Brit on a Friday. The pain of a Brit so close to Shabbat would detract from the Oneg (enjoyment) Shabbat of the baby. Hacham Ovadia concurs with this opinion.

Based on these Halachot, the question was posed with regard to a baby born during the twilight hour between Wednesday and Thursday. In such a case, it cannot be clearly determined whether the birth was on Wednesday or Thursday. Therefore, out of doubt, the Halacha assumes the birth to be on the later day, Thursday, and the eighth day would be the following Thursday. Would such a Brit be considered "postponed" and therefore prohibited, according to the Tashbes?

Hacham David rules that it would be permitted. He reasons that there is a Safek Sefeka (Double Doubt) in favor of performing the Brit on Thursday: First, perhaps the Halacha is not in accordance with the stringent opinion of the Tashbes, but rather like the other lenient opinions that always permit a postponed Brit on Thursday. Second, even if the Halacha is like the stricter opinion, perhaps the twilight birth is actually considered to be on Thursday, in which case the Brit is not postponed, but in its proper time.

SUMMARY: It is prohibited to perform a postponed Brit on Shabbat, Thursday or Friday.

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