Fiqh-us-Sunnah Volume 2, Supererogatory Prayer, Fiqh 2.006A.

‘Aishah says: “After the Prophet had prayed the two [sunnah] rak’at of the fajr, he would lie down on his right side.” This is related by the group. They also record that she reported: “After the Messenger of Allah had prayed the two [sunnah] rak’at of the fajr, he would lie down if I was asleep or would talk to me if I was awake.”

There is quite a difference of opinion over this point. Apparently, it is preferred for one to do so if one prays these sunnah rak’at in one’s house and not in the mosque. Ibn Hajar says in Fath al-Bari: “Some of the early scholars were of the opinion that it is preferred to do so if one prays in one’s house rather than in the mosque.” This has been recorded from Ibn ‘Umar. Some of our scholars reinforce this argument by stating that there is no evidence that the Prophet ever did so in the mosque. It has also been authentically recorded from Ibn ‘Umar that “he would throw pebbles at anyone who did so in the mosque,” and this was related by Ibn Abi Shaibah. Imam Ahmad was asked about it and he said: “I do not do it but if a person does it, it is good.”