When the muezzin finished the first call to prayer for Fajr, the Messenger of Allah ﷺ would rise and pray two brief units before the Fajr prayer, after the dawn had clearly appeared, then he would lie down on his right side.
أخبرنا عمرو بن منصور قال حدثنا علي بن عياش قال حدثنا شعيب عن الزهري قال أخبرني عروة
كان رسول الله ﷺ إذا سكت المؤذن بالأولى من صلاة الفجر قام فركع ركعتين خفيفتين قبل صلاة الفجر بعد أن يتبين الفجر ثم يضطجع على شقه الأيمن
Bukhari reported it in the Book of Adhan, chapter of one who waits for the iqama, hadith no. 626, from the hadith of Shuayb bin Abu Hamza, and Muslim in the Book of the Prayer of Travelers, chapter on the night prayer and the number of units of prayer the Prophet ﷺ performed at night, and so on, hadith no. 122/736, from the hadith of Zuhri with the same wording, and it is in Kubra, hadith no. 1455.