What is the ruling on specifically singling out the fifteenth day of Sha'ban for fasting?

Fasting on the 15th of Sha'ban has not been reported in the Prophetic Sunnah or the actions of the Companions; it is an innovated matter. An exception to this is for those who have a customary fast, such as fasting alternate days, or the White Days, or Mondays and Thursdays, or one who vowed a fast and it coincided with that day.