Authenticity of Fasting During Rajab

Fasting during the month of Rajab is highly recommended (Mustahab) in Shari'ah. As it is mentioned in Fataawa Hindiyyah:

Translation: "There are several types of recommended fasts: the first is the fast of Muharram, the second is the fast of Rajab, the third is the fast of Sha’baan, and the fourth is the fast of Ashura." (Fatawa Hindiyyah, Volume 1, Page 222, Book Of Fasting/Darul Kutbul Ilmiyyah, Beirut)

And it is stated in Al-Fiqhu Alal-Madhaahibil-Arbaʿah:

Translation: "It is recommended to fast in the months of Rajab and Shaʿbaan." (Al-Fiqhu Alal-Madhaahibil-Arbaʿah, Volume 1, Page 507, Darul Kutbul Ilmiyyah, Beirut) Fasting in Rajab is also established from the Blessed Practice of the Holy Prophet صلى الله عليه وسلم. As it is narrated in Muslim Shareef:

Translation: Hazrat Uthmaan bin Hakeem Ansaari states: I asked Saʿeed bin Jubair about fasting in Rajab while we were in the month of Rajab. He said: I heard Hazrat Ibn e Abbaas RadiAllahu Anhuma say: "The Messenger of Allah صلى الله عليه وسلمused to fast continuously; when He صلى الله عليه وسلم stopped, we thought He صلى الله عليه وسلمwould never fast again, and when He صلى الله عليه وسلم broke His صلى الله عليه وسلمfast, we thought He صلى الله عليه وسلمwould never fast again." (Saheeh Muslim Shareef, Book Of Fasting, Volume 2, Page 811)

The virtues of fasting in Rajab have been further highlighted by Allamah Sheikh Ali bin Sultan Muhammad Al-Qari Alaihir Rahmah in his book Al-Adabu Fee Rajab, where he cites several Hadiths. A few key narrations are:

Translation: "Indeed, Rajab is a great month, in which good deeds are multiplied. Whoever fasts one day of it, it is as if he has fasted for an entire year." This Hadith is reported in the Marfoo form by Raafaʿee and Ibn e Abbaas. (Al-Adabu Fee Rajab, Page 30, with reference to Al Muʿjamul Kabeer)

Translation: "Indeed, there is a river in Paradise called Rajab. Its water is whiter than milk and sweeter than honey. Whoever fasts one day in the month of Rajab, Allah Almighty will let him drink from this river." Narrated by Bayhaqi. (Al-Adabu Fee Rajab, Page 32) For further study and detailed references, reading Allamah Sheikh Ali bin Sultan Muhammad Qari’s Al-Adabu Fee Rajab is highly recommended.