I observe every second person in the mosque on daily basis, perform two Raka'a Sunnah after the Fajr Farz Salah almost all over the kingdom (Saudi Arabia). As far I know there is no Salah after far Farz prayers and once the Prophet (Sallallahu Alaihi wa Sallam) had performed Qadha of Fajr prayers, he first said two Raka'a Sunnah and than Farz. Isn't it that theses two Sunnah one can say after once in blue moon and not every day. To me this is next to Bida'h.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

The Fajr Sunnah should be prayed before Fajr obligatory prayer. So, anyone who performs it after Fajr without any excuse commits an innovation in religion. But if the person has an excuse for praying Fajr Sunnah after Fajr prayer or after sunrise, then he can do so. The evidence for this is the Hadeeth of Qays ibn Fahd who said: “The Prophet saw me performing two Rak'ahs after finishing the Fajr prayer. He asked: “What are these two Rak'ahs?' "What is this prayer?" I said: “O Messenger of Allah! I did not perform the two Rak'ahs that precede the prayer of Fajr, so I performed them now.” [Ahmad, Abu Dawood and at-Tirmithi]

Since the Prophet did not comment on this, it becomes lawful to do so when there is a necessity. The Prophet also said in another Hadeeth: “Whoever misses to pray the two Rak'ahs of Fajr Sunnah, then he should pray them after sunrise.” [At-Tirmithi]

For more benefit on praying two Rak'ahs Sunnah before Fajr obligatory Prayer, please refer to Fatawa 85611 and 84847.

Allah knows best.