The Messenger of Allah ﷺ used to sleep during the early part of the night and spend the latter part of it in worship.
حدثنا أبو بكر بن أبي شيبة حدثنا عبيد الله عن إسرائيل عن أبي إسحق عن الأسود
كان رسول الله ﷺ ينام أول الليل ويحيي آخره
Bukhari narrated it in the Book of Tahajjud, Chapter on One Who Sleeps at the Beginning of the Night and Stays Awake in Its Latter Part, hadith no. 1146, and Muslim, hadith no. 739, from the Book of the Prayer of Travelers, Chapter on the Night Prayer and the Number of Units the Prophet ﷺ Prayed at Night, the hadith of Abu Ishaq, with this same wording.