It is preferred to fast the three bright days, namely the 13th, the 14th, and the 15th. They are also said to be the 12th, the 13th, and the 14th. The first opinion is the more correct and famous.
1258/1 - Abu Hurayrah (may Allah be pleased with him) said: “My close friend (may Allah’s peace and blessings be upon him) advised me to observe fast for three days in every month, to perform the two Rak‘ahs of the Duha prayer, and to perform the Witr prayer before going to bed.” [Narrated by Al-Bukhāri and Muslim]
1259/2 - Abu al-Dardā’ (may Allah be pleased with him) reported: “My beloved (may Allah’s peace and blessings be upon him) advised me to do three things which I would never abandon as long as I live: fasting three days every month, offering the Duha prayer, and not going to bed before performing the Witr prayer.” [Narrated by Muslim]
1260/3 - ‘Abdullāh ibn ‘Amr ibn al-‘Ās (may Allah be pleased with him and his father) reported that the Messenger of Allah (may Allah’s peace and blessings be upon him) said: “Fasting three days every month is fasting the whole year.” [Narrated by Al-Bukhāri and Muslim]
1261/4 - Mu‘ādhah al-‘Adawiyyah reported that she asked ‘Ā’ishah (may Allah be pleased with her): “Did the Messenger of Allah fast three days every month?” ‘Ā’ishah replied: “Yes.” Mu‘ādhah asked: “In which part of the month did he fast?” ‘Ā’ishah replied: “It did not matter to him in which part of the month he fasted.” [Narrated by Muslim]
1262/5 - Abu Dharr (may Allah be pleased with him) reported: The Messenger of Allah (may Allah’s peace and blessings be upon him) said: “If you fast three days in a month, then fast the thirteenth, fourteenth, and fifteenth.” [Narrated by Al-Tirmidhi; and he classified it as Hasan (sound)]
1263/6 - Qatādah ibn Milhān (may Allah be pleased with him) reported: “The Messenger of Allah (may Allah’s peace and blessings be upon him) used to command us to fast the bright days: the thirteenth, the fourteenth, and the fifteenth.” [Narrated by Abu Dāwūd]
1264/7 - Ibn ‘Abbās (may Allah be pleased with him and his father) reported: “The Messenger of Allah (may Allah’s peace and blessings be upon him) would not fail to fast the bright days whether he was residing or traveling.” [Narrated by Al-Nasā’i with a sound Isnād]
1) Fasting three days every month is equivalent to fasting the whole year, for a good deed is rewarded by ten times as much.
2) Fasting the three days in the middle of the month - 13, 14, and 15 - is the best form of fasting, for this was the more frequent practice of the Prophet (may Allah’s peace and blessings be upon him).
3) They show the merit of the Companions, as they were keen to act upon the Prophet’s instructions throughout their lives.