What is the best time for performing

Q 2: What is the best time of the night to offer Tahajjud (optional late night Prayer)? Every night, I wake up just half an hour before the Fajr (Dawn) Prayer to offer Salah (Prayer), two Rak`ahs (units of Prayer) at a time. When I hear the Adhan (call to Prayer), I conclude with Witr (Prayer with an odd number of units). Shall I go on doing this and be rewarded for Qiyam-ul-Layl (optional Prayer at night), or is there a better time to offer Salah, such as the middle of the night for instance? Please advise.

(Part No. 7; Page No. 222)  A: The best time to offer Qiyam-ul-Layl is the late part of the night, as the Prophet (peace be upon him) stated: The most beloved Salah to Allah was that of Dawud (David) who used to sleep for (the first) half of the night, offer Salah for one third of it, and sleep for a sixth of it... He (peace be upon him) also stated: Our Lord descends every night to this heaven when the last third of the night begins. He says: Is there any supplicant to answer them? Is there any seeker for My Favor to give them? Is there any seeker for forgiveness to forgive them? Agreed upon their authenticity. This descent mentioned in the Hadith occurs in a manner befitting the Majesty and Magnificence of Allah; none of His creatures resemble Him in this, as Allah stated: There is nothing like Him; and He is the All-Hearer, the All-Seer. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.