Megillah 30B

ואיזו היא שבת רביעית ⁠— כל שחל ראש חדש ניסן להיות בתוכה, ואפילו בערב שבת.

And which is the 4th Shabbat? The Shabbat of whichever week during which Rosh Chodesh of Nisan occurs, and this is the case even if it occurs on Friday.

בחמישית חוזרין לכסדרן וכו׳. לסדר מאי? רבי אמי אמר: לסדר פרשיות הוא חוזר. רבי ירמיה אמר: לסדר הפטרות הוא חוזר.

§ The Mishnah states: On the fifth Shabbat, we resume the regular weekly order. The Talmud clarifies the Mishnah’s intent: To the order of what does one resume? R' Ami said: One resumes the regular weekly order of Torah portions. R' Ami holds that on the weeks on which the special portions are read, the regular weekly Torah portion is not read at all, and therefore the cycle is resumed only on the fifth Shabbat. R' Yirmeya said: One resumes the regular weekly order of the haftarot. R' Yirmeya holds that even on the Shabbatot on which the special portions are read, the regular weekly portion is still read; the special portion is read by the last reader as the maftir. However, the haftara of the regular cycle is entirely replaced with a portion from the Prophets that parallels the special portion. As such, it is the cycle of haftarot that is resumed on the fifth Shabbat.

אמר אביי: כוותיה דרבי אמי מסתברא, דתנן: לכל מפסיקין, לראשי חדשים, לחנוכה, ולפורים, לתעניות, ולמעמדות, וליום הכפורים.

Abaye said: It stands to reason that one should rule in accordance with the opinion of R' Ami, as we learned in the Mishnah: For all special days, we interrupt the regular order of readings, and a special portion relating to the character of the day is read. This applies to the New Moons, to Hanukkah, and to Purim, to fast days, and to non-priestly watches, and to Yom Kippur.