There is no authentic hadith about the virtue of Rajab. The hadith which reads: “Allhumma barik lana fi Rajab wa Sha’ban wa ballighna Ramadan” is weak. However, there is nothing wrong if a Muslim asks Allah to let him reach Ramadan. For more, please see the detailed answer.

What is narrated about praying, fasting and worshipping on the 15th of Sha’ban is fabricated. So it is not permissible to follow such hadiths or to act upon them, whether that is in doing righteous deeds or otherwise. For more, please see the detailed answer.