Salat Al-Fajr has specific sunan, from among them are:
Shorten the Length of Sunnah Prayer:
On the authority of ‘Aishah radhiAllahu ‘anha:
“The Prophet salAllahu ‘alayhi wa sallam prayed two short Ra’kah between the Athaan and Iqamah of Fajr prayer.”
Recommended Ayaat to recite in the Sunnah Prayer:
Rest after the Sunnah Prayer:
When the Prophet salAllahu ‘alayhi wa sallam prayed two ra’kah of the Sunnah prayer of Al-Fajr, he would lie down on his right side. [The general practice of the Prophet salAllahu ‘alayhi wa sallam was to pray the Sunnah prayer at home.]
After you have prayed the two ra’kah of the Sunnah of Al-Fajr, try to lie down on your right side, even for a minute or so, so that you can fulfill this Sunnah.
*Dr. Muhammad Salah of Huda TV comments that the reason the Prophet salAllahu ‘alayhi wa sallam used to rest between Sunnah and Fard prayer was that he spent the last part of the night standing in prayer (Tahajjud). If we have not prayed the Tahajjud prayer or made a long qiyaam then this rest makes no sense.
Sitting after the Fajr Prayer:
It is from the Sunnah to sit after the prayer:
When the Prophet salAllahu ‘alayhi wa sallam prayed Fajr, he sat in his place until the sun rose hassanaa.
Imam An-Nawawi explains hassanaa means ‘risen perfectly’.
Benefits of Sitting in Masjid:
Allah subhanahu wa ta’ala instructed the angels to pray for forgiveness for those sitting in the Masajid whether it is before or after the Salah.
*The time you spend sitting on the prayer rug, engaged in thikr or waiting for the next Salah, the angels keep praying for you. They say, “O Allah! Forgive him,” and “O Allah! Have mercy on him.”
What is a greater blessing than this? Look at your status with Allah subhanahu wa ta’ala if you obey Him, the angels – the creation that is close to Allah – are instructed to supplicate for you!
[Book: More than 1000 Sunan Every Day and Night (Adhkar Min Alf Sunnah Fee Al-Yawm Wa Al-Laylah, Dar-us-Salaam Publications)]