All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger, may Allah exalt his mention as well as that of his family and all his companions.
The actions of people are presented to Allah in the month of Sha’ban, so the Prophet sallaAllahu alaihi wa sallam used to fast repeatedly in this month. ‘Aishah said: "I never saw the Messenger of Allah fast for a complete month except for Ramadan, and I never saw him do more fasting in any month than he did in Sha’ban". [Al-Bukhari and Muslim]
Usamah bin Zaid, may Allah be pleased with him, reported "I said to the Prophet, O Messenger of Allah! I did not see you fasting in any month as you do in the month of Sha’ban". The Prophet sallaAllahu alaihi wa sallam said: "People neglect this month which is between Rajab and Ramadan, in this month the actions of the people are presented to Allah; so I like my deeds to be presented while I am fasting". [Abu Dawood, An-Nasai]
As for fasting particularly the fifteenth of Shaban this is not proved through any sound evidence. There are some sayings of the companions of the Prophet and their successors, may Allah be pleased with them, which indicate the virtue of this night. But this does not mean that there is any special significance to the day or that night. So, there is no evidence proving that fasting such a day is Sunnah nor is there any evidence proving that there are some specific prayers to be performed at the fifteenth night of Sha’ban.