Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is sunnah to fast:
- six days of Shawwal,
- three days (preferably the 13th, 14th, and 15th) of any given month,
- every Monday or Thursday (or both),
- on the 10th of Muharram (known as the day of Ashura), and
- on the first nine days of Dhul Hijjah (with the 9th (Day of Arafah) being more emphasized).
Answering your question, Sheikh Mustafa Umar, President of California Islamic University, states:
It is recommended to fast six days of Shawwal, to fast three days (preferably the 13th, 14th, and 15th) of any given month (of the lunar calendar), to fast every Monday or Thursday (or both), to fast on the 10th of Muharram (known as the day of Ashura), and to fast on the first nine days of Dhul Hijjah (with the 9th being more emphasized).
Do not fast on the day of Eid al-Fitr, Eid al-Adha, and on the 11th, 12th, and 13th of Dhul Hijjah. Also, do not fast every day with the intention to continue throughout your life or to fast for two days straight without breaking the fast in between.
Prophet Muhammad (peace be upon him) said:
“Whoever fasted Ramadan and then followed it up with six days of Shawwal, it is as if he fasted continuously.” [Muslim]
“Fast some days of the sacred months and not others.” [Abu Dawud, graded weak by several scholars]
Imam Ibn Taymiyyah said:
“As for fasting in Rajab specifically, the hadiths about that are all weak, actually they are fabricated. The scholars do not rely on any of them. They are not among the weak hadiths which have been narrated about virtues, rather most of them are fabricated and false.
In Al-Musnad and elsewhere, there is a hadith which says that the Prophet encouraged fasting the sacred months, namely Rajab, Dhul-Qidah, Dhul-Hijjah and Muharram, but this has to do with fasting during all of them, not just Rajab.” [Majmu` Al-Fatawa, 25:290]
Imam Ibn al-Qayyim said:
“Every hadith which mentions fasting in Rajab and praying during some of its nights is false and fabricated.” [Al-Manar al-Munif, 96]
Almighty Allah knows best.
Source: AsktheScholars.com