What is the ruling on praying two supererogatory rak'ahs after the Fajr adhan, before performing the obligatory prayer, other than the Sunnah of Fajr?

There is no supererogatory prayer after the dawn breaks except for the two rak'ahs of Fajr. Some scholars have held the view that it is permissible to pray supererogatory prayers for one who missed the night prayer, and this is the opinion of Al-Hasan and Malik.