Related for Megillah 59:24
ברביעית (שמות יב, ב) החדש הזה לכם: תנו רבנן ר"ח אדר שחל להיות בשבת קורין כי תשא ומפטירין ביהוידע ואי זו היא שבת ראשונה כל שחל ר"ח אדר להיות בתוכה ואפילו בערב שבת בשניה זכור ומפטירין (שמואל א טו, ב) פקדתי ואי זו היא שבת שניה כל שחל פורים להיות בתוכה ואפילו בערב שבת
On the fourth, “this month shall be for you” (Exodus 12:2). Our Rabbis taught: If Rosh Hodesh Adar falls on Shabbat, we read Ki Tisa and as haftarah [the portion about] Yehoyada. Which is the first Shabbat? The one on which Rosh Hodesh Adar falls in the following week, even if on Friday. On the second Shabbat Zakhor is read, and for haftarah, “I have visited” (II Samuel 15:2). Which is the second Shabbat? The one in which Purim falls in the following week, even if on Friday.
Tosefta Megillah
[When] Rosh Chodesh Adar falls on Shabbat, we read the portion of "Shekalim" (Ex. 30:11-16) and in addition we read the portion of the shekalim that concerns Yehoyada the Kohen (commencing with 2 Kings 12:8). What is the "first Shabbat"? Any Rosh Chodesh Adar falls within [that designation], even on Erev Shabbat. On the second Shabbat, [we read the portion beginning] "Remember [what Amalek did]" (Deut. 25:17) and additionally we read "Thus said the Lord of Hosts, I remember what Amelek did to Israel" (1 Sam. 15:2). What is the "second Shabbat"? Every [Shabbat] in which Purim falls within it, and even on Erev Shabbat. On the third [Sabbath we read the portion of] the Red Heifer, and additionally we read "And I will sprinkle pure water on you and you will be purified" (Ezek. 36:25). What is the "third Shabbat"? Any [Shabbat] that immediately follows Purim. The fourth [Shabbat we read], "This month shall be to you the head of the months" (Ex. 12:2), and in addition [we read] "Thus said the Lord, in the first [month], on the first of the month" (Ezek. 45:18). Which is the fourth Shabbat? Any [Shabbat] in which Rosh Chodesh Nissan falls within it, and even on Erev Shabbat.
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