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:
There is no basis for this hadith in the books of Sunnah and reports, and no narration is known for it with any of the scholars.
Answering your question, the Fatwa Center at Islam Q and A, states:
There is no basis for this hadith in the books of Sunnah and reports, and no narration is known for it with any of the scholars. Similarly, we could not find it in the books which deal with false and fabricated hadiths.
It was mentioned by Ibn Tawus – Ali ibn Musa ibn Jafar (d. 664 AH) – in his book Iqbal al-Amal (3/216). But we did not find any basis for this hadith in any earlier book of the Shi`ah. Ibn Tawus mentioned it in a comment without any isnad, and said:
“Chapter on what we have mentioned about the virtue of seeking forgiveness, repeating La ilaha ill-Allah and repenting in the month of Rajab. We found this narrated from the Prophet that he said: “Whoever says in Rajab ‘I ask Allah for forgiveness, there is no God but He alone, with no partner or associate, and I repent to Him’ one hundred times, and ends it with charity, Allah will decree for him mercy and forgiveness. And whoever says it four hundred times, Allah will decree for him the reward of one hundred martyrs, and when he meets Allah on the Day of Resurrection, He will say to him: You affirmed My sovereignty, so wish for whatever you want so that I may give it to you, for there is none who prevails but Me.”
It was transmitted from him in some of the other books, such as Wasa’il ash-Shi`ah (10/484) by al-Hurr al-`Amili (d. 1104 AH) and others.
Thus the signs of fabrication in this hadith become clear:
The hadith is devoid of any isnad.
It is only the books of the Rafidah that mention this hadith. From their books, the hadith has become well known in some Internet chat rooms and websites. Hence it is essential to be cautious about many of the hadiths that are quoted in chat rooms when their sources are the fabricated books of the Rafidis.
The hadith has to do with the virtues of the month of Rajab. We must be cautious about all reports that speak of this matter, because there are so many fabricated reports concerning it that some of the scholars wrote books dealing specifically with that, such as Al-Hafizh Ibn Hajar (may Allah have mercy on him) in his book Tabyeen al-`Ajab bima warad fi Fadl Rajab. He (may Allah have mercy on him) said:
No sound hadith that is fit to be used as evidence has been narrated concerning the virtues of the month of Rajab or of fasting that month or any specific part of it, or praying qiyam al-layl specifically during that month. This has been stated categorically before me by Imam Abu Ismail al-Harawi al-Hafizh, and we have narrated it from him with a sahih isnad as we also narrated it from others. But it is well known that the scholars are deviant in narrating hadiths about virtues, even if they are da`eef, so long as they are not fabricated. Nevertheless we should stipulate that the one who does that should believe that the hadith is weak and he should not make it well-known, lest people act upon a weak hadith and prescribe something that is not prescribed, or lest some of the ignorant see that and think that it is a sahih Sunnah.” (Tabyeen al-`Ajab, p. 11)
Exaggeration about the reward, whereby a small deed in the month of Rajab is said to bring the reward of one hundred martyrs and more. Such as it is not narrated in the sahih reports.
Almighty Allah knows best.