Is it permissible to count staying up late for sharia studies as part of qiyam al-layl (night vigil), or is qiyam al-layl limited to prayer, reciting the Quran, and dhikr (remembrance of Allah) only, and what intention makes staying up late for studies a source of reward?

Studying sacred knowledge and staying up late for it is one of the best forms of worship if the intention is sincere. Scholars have explicitly stated that engaging in knowledge is better than supererogatory acts of worship, provided that the intention for seeking knowledge is sincere. Therefore, a female student staying up late to study is considered a form of enlivening the night in worship, and its reward is no less than other acts of worship, with the intention of pleasing Allah and dispelling ignorance.