There is not any authentic evidence that supports making a special Du‘a’ or act of worship on the fifteenth night of Sha‘ban. Doing this is a Bid‘ah (innovation in religion).
Celebrating the 15th night of Sha‘ban is a Bid‘ah (innovation in religion) and so is the celebration of the twenty-seventh night of Rajab which some peoplecall the Night of Isra’ (Night Journey) and Mi‘raj (Ascension to Heaven).
According to the expert scholars who verify Hadith, there is no Hadith ranked as Sahih among those narrated about the merits of spending the night of the middle of Sha‘ban in Salah and the day in Sawm. Thus, they negated the merits of spending the night in Salah and the day in Sawm, and considered this a Bid‘ah (innovation in religion).
The Prophet (peace be upon him) said: Every newly-introduced matter is a Bid‘ah and every Bid‘ah is a Dalalah (deviation from what is right).
[Bukharee and Muslim]