Staying awake in Shab Bara'at and spending the night in prayer.
Worship of any kind in Shab Bara'at is established by the Hadith. There is a Hadith in Ibn Majah:
Translation: It has been narrated on the authority of Hadhrat Ali Murtuza (May Allah SWT be well pleased with him) that the Holy Prophet (Sallallahu alaihi wa sallam) said: When the 15th night of Sha'aban comes, stand in prayer in the night and fast in its day, because that night Allah (Subhanahu Wa Ta'ala) graces the skies of this world with His presence right from sunset and says: Is there anyone who desires forgiveness that I may forgive him (or her)? Is there anyone who desires Rizq that I may grant it? Is there anyone plagued by some difficulty that I may grant comfort? Is there anyone like this? Until the Fajr dawns.
This Hadith shows the praying in the night of Sha'aban and fasting the next day to be a Sunnah. That Allah (Subhanahu Wa Ta'ala) graces the skies of this world means that Allah (Subhanahu Wa Ta'ala) spreads His mercy or that He turns from His attributes of "Jalal" to His attributes of "Jamal," as He wishes to.