Hadith: The Messenger of Allah (may Allah's peace and blessings be upon him) used to pray two light Rak‘ahs before the Fajr prayer, after the Muezzin would finish calling the Adhān and after the break of dawn. Then, he used to lie on his right side until the Muezzin would come to him for the Iqāmah

عن عائشة رضي الله عنها قالت: «كان رسول الله صلى الله عليه وسلم إذا سَكَتَ المؤذن بالأولى من صلاة الفجر قام، فركع ركعتين خفيفتين قبل صلاة الفجر، بعد أن يَسْتَبينَ الفجر، ثم اضطجع على شِقِّهِ الأيمن، حتى يأتيه المؤذن للإقامة».
[صحيح] - [متفق عليه]

‘Ā'ishah (may Allah be pleased with her) reported: The Messenger of Allah (may Allah's peace and blessings be upon him) used to pray two light Rak‘ahs before the Fajr prayer, after the Muezzin would finish calling the Adhān and after the break of dawn. Then, he used to lie on his right side until the Muezzin would come to him for the Iqāmah.
Sahih/Authentic. - [Al-Bukhari and Muslim]

Explanation

This noble Hadīth clarifies that whenever the Adhān for the Fajr prayer was made, the Prophet (may Allah's peace and blessings be upon him) would pray two Rak‘ahs, then lie on his right side until the Muezzin would come to him for the Iqāmah.