Is it better to pray at the beginning of the night with vigor and energy and recite more, or to pray at the end of the night with difficulty, less reflection, and less recitation? And does the reward for recitation increase in the last third of the night?

The best time for Qiyam al-Layl (night vigil prayer) is the latter half of the night, and the best of it is the prayer of David (peace be upon him): he would sleep half the night, stand in prayer for a third of it, and sleep for a sixth. Nevertheless, if praying in the early part of the night is more invigorating and allows for greater reflection, then it is better in that case.

It is permissible to dedicate the end of the night (waqt al-sahar – the pre-dawn time) for seeking forgiveness and supplication, and this is good and recommended, due to the Almighty's saying: "And in the dawns, they used to ask for forgiveness" (Adh-Dhariyat: 18), and due to Allah's descent to the lowest heaven in the last third of the night.

The reward for reciting the Quran increases in the last third of the night, and it is the best time for Quranic recitation.