What is the most excellent time for Tahajjud prayer?

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The last third of the night is the best time for Tahajjud. This is supported by the narration from Amr ibn Absa, where the Prophet peace be upon him stated that the latter part of the night is when one's supplication is most likely to be heard. The most virtuous prayer is the prayer of Dawud, which involved sleeping for half the night, praying for one-third, and sleeping for one-sixth. The Prophet's practice often involved sleeping until the middle of the night or slightly before or after, waking to perform Tahajjud until the time of the first call to prayer (Adhan) for Fajr. The reason for this preference is that the Lord descends to the lowest heaven during the last third of the night, answering those who call upon Him, granting what is asked, and forgiving those who seek His forgiveness, as narrated by Abu Hurairah. If the worshipper manages to sleep after Tahajjud, the effects of sleeplessness do not show; otherwise, they do.