The Prophet, peace and mercy be upon him, said, “There are five nights in which du’a (supplication) is not rejected: the eve of
Rajab, the 15th night of Sha’aban, the eve of Friday, on the eve of Eid Al-Fitr, and on the eve of Eid Al-Adha.” [Al-Suyuti in his Al-Jami’].
The Prophet, peace and mercy be upon him, said, “Rajab is the month of Allah, and Sha’aban is my month, and Ramadan is the month of my Ummah.” (Imam Al-Suyuti in Al-Jami).
and the hadith which states that he would enobble and fast the month of rajab
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These are not authentic.