Fiqh-us-Sunnah Volume 3, Zakaat and Fasting, Fiqh 3.127A.

The “forbidden” months (during which killing is forbidden) are Zhul-Qidah, ZhulHijjah, Muharram, and Rajab. It is preferred to fast a lot during these months.

A man from Bahila came to the Prophet and said: “O Messenger of Allah, I am the man who came to you during the first year.” The Prophet, upon whom be peace, said: “What has changed you? You used to be much more handsome!” He answered: “I did not eat save during the night since I left you.” The Messenger of Allah asked: “Why did you punish yourself? Fast during the month of patience [that is, Ramadan] and then one day of every month.” The man said: “Add something to that for me, for I have more strength than that.” The Prophet responded: “Fast two days [a month].” The man said: “Add more for me.” The Prophet said three times: “Fast from the forbidden months, then leave fasting.” He pointed with three of his fingers by clenching them and releasing them. This is related by Ahmad, Abu Dawud, Ibn Majah, and al-Baihaqi with a good chain.

Fasting during Rajab contains no more virtue than during any other month. There is no sound report from the sunnah that states that it has a special reward. All that has been related concerning it is not strong enough to be used as a proof. Ibn Hajr says: “There is no authentic hadith related to its virtues, not fasting during it or on certain days of it, nor concerning exclusively making night prayers during that month.”