I came to Aswad bin Yazid, who was a brother and close friend to me, and said, "Abu Amr, tell me what Umm Muiminin told you about the prayer of the Messenger of Allah ﷺ."He said, "She said that he would sleep during the first part of the night and stay awake in worship during its latter part."
أخبرنا محمد بن عبد الله بن المبارك قال حدثنا يحيى قال حدثنا زهير
أتيت الأسود بن يزيد وكان لي أخا صديقا فقلت يا أبا عمرو حدثني ما حدثتك به أم المؤمنين عن صلاة رسول الله ﷺ قال قالت كان ينام أول الليل ويحيي آخره
Recorded by Muslim, Prayer of the Traveler, chapter on night prayer and the number of units of prayer the Prophet ﷺ performed at night, etc., no. 739, from the hadith of Zuhayr bin Ishaq, and Bukhari, Tahajjud, chapter on one who sleeps at the beginning of the night and stays awake in its later part, no. 1146:6, from the hadith of Abu Ishaq, through him. It is also in Kubra, no. 1309.