Ibn al-Qayyim (may Allaah have mercy on him) said: “Every hadeeth which mentions fasting in Rajab and praying during some of its nights is false dan fabricated.” (al-Manaar al-Muneef, p.96)
The fasting that is prescribed in Rajab is the same as that prescribed in other months, namely fasting on Mondays and Thursdays, and the three days of al-Beed, fasting alternate days, and fasting Sirar al-Shahr. Some of the scholars said that Sirar al-Shahr refers to the beginning of the month; others said that it refers to the middle or end of the month.
‘Umar (may Allaah be pleased with him) used to forbid fasting in Rajab because it involved resemblance to the Jaahiliyyah. It was reported that Kharashah ibn al-Harr said: I saw ‘Umar smacking the hands of those who fasted in Rajab until they reached out for food, and he was saying, This is a month which was venerated in the Jaahiliyyah. (al-Irwaa’, 957; al-Albaani said: it is saheeh).
Imaam Ibn al-Qayyim said: the Prophet SAWS (peace and blessings of Allaah be upon him) did not fast for three consecutive months (i.e., Rajab, Sha’baan and Ramadaan) as some people do, and he never fasted Rajab at all, nor did he encourage people to fast this month.
Al-Haafiz ibn Hajar said in Tabayyun al-‘Ajab bimaa wurida fi Fadl Rajab:
No saheeh hadeeth that may be used as evidence has been narrated concerning the virtues of the month of Rajab or fasting this month or fasting in any specific part of it, or observing Qiyaam al-Layl specifically during this month. Imaam Abu Ismaa’eel al-Harawi al-Haafiz has already stated this before me, and we have narrated this from others also.
In Fataawa al-Lajnah al-Daa’imah it states: with regard to fasting specifically in Rajab, we do not know of any basis in Sharee’ah for doing that.