Authentic Supplication Number 49.
The Prophet said: “There is in the night a time such that during it no Muslim man asks Allah to Whom belongs Glory and Power for some Good of the affairs of this Life or the Hereafter; except that Allah would grant him it, and that is every night”. Allah The Exalted said: “And those who pray for forgiveness in the early hours of the morning” (72).
(72) Surat Ale-`lmran (#3) V.17.
Reported by Muslim, and is in The Authentic of Good Sayings as #43.