What is the ruling on fasting the last three days of the month, and is it narrated that the Prophet, may God's prayers and peace be upon him, fasted them?

The Prophet, peace and blessings be upon him, encouraged fasting three days every month, and in some narrations, he did not specify particular days, so he would fast them at any time during the month.

Other narrations state that he used to fast the beginning of the month, or the "White Days" (the thirteenth, fourteenth, and fifteenth).

As for fasting the last days of the month (the "Black Days"), there is no explicit hadith indicating its فضيلة (merit). Rather, some scholars inferred its desirability from the hadith of Imran ibn Husayn, in which the Prophet, peace and blessings be upon him, was asked about fasting the "surar of this month," and the majority interpreted "surar" as the end of the month. Some scholars, such as Ibrahim al-Nakha'i and some Shafi'is, recommended fasting these days to be an atonement for sins, and there is no harm for whoever fasts them.