On the authority of ʿĀʾishah (may Allah be pleased with her), who said: When the Prophet ﷺ had prayed the two rakʿahs of the dawn prayer, he would lie down on his right side. Narrated by al-Bukhārī.
١٩٨ - باب استحباب الاضطجاع بعد ركعتي الفجر على جنبه الأيمن والحث عليه سواء كان تهجد بالليل أم لا
On the authority of ʿĀʾishah (may Allah be pleased with her), who said: When the Prophet ﷺ had prayed the two rakʿahs of the dawn prayer, he would lie down on his right side. Narrated by al-Bukhārī.
And on her authority, she said: The Prophet ﷺ used to pray, in the time between finishing the night prayer (ʿishāʾ) and the dawn, eleven rakʿahs, giving the salutation (taslīm) after every two rakʿahs and praying witr with a single one. Then, when the muezzin had fallen silent after the call for the dawn prayer, the dawn had become clear to him, and the muezzin had come to him, he would rise and pray two brief rakʿahs; then he would lie down on his right side, [remaining] thus until the muezzin came to him for the iqāmah. Narrated by Muslim. Her words, "he gives the salutation between every two rakʿahs," are thus in Muslim, and their meaning is: after every two rakʿahs.
And on the authority of Abū Hurayrah (may Allah be pleased with him), who said: The Messenger of Allah ﷺ said: "When one of you has prayed the two rakʿahs of the dawn prayer, let him lie down on his right side." Narrated by Abū Dāwūd and al-Tirmidhī with sound chains of transmission. Al-Tirmidhī said: "A good and sound hadith (ḥasan ṣaḥīḥ)."