The best time to perform Tahajud (night vigil prayers) is in the last portion of the night just before the fajr (dawn) prayer.
The Prophet Muḥammad (peace and blessings upon him) is reported to have declared, “The prayer in the last portion of the night is witnessed [by angels] and that is superior [in blessings]”. (Ṣaḥīḥ Muslim)
And Allah knows best.
Answered by Shaykh Yusuf Badat Hadith of the Day Imam Imam of the Islamic Foundation of Toronto and Director of Mathabah Institute