Whenever the Messenger of Allah ﷺ prayed the two rakahs of Fajr, he would lie down on his right side.
حدثنا عبد الله بن يزيد قال سعيد يعني ابن أبي أيوب حدثنا أبو الأسود عن عروة
كان رسول الله ﷺ إذا صلى ركعتي الفجر اضطجع على شقه الأيمن
Its isnad is sahih. Abu Aswad is the orphan raised by Urwa, and his name is Muhammad bin Abdul-Rahman bin Nawfal Asadi. The hadith has already appeared in 24890.