Answered by Shaykh Faraz Rabbani
In what situation should one pray the 2 sunna of Fajr if the congregation has already started its prayer?
The Beloved of Allah (Allah bless him and give him peace) said,
“The two [sunna] rakats of Fajr are better than the world and all it contains.”
If one has not prayed the sunna of fajr when one enters the mosque and finds the congregation in progress, one should perform it, as long as one can catch any part of the fard with the imam and no fitna is feared from people objecting. However, one should do so away from the lines of the congregation itself. [Ibn al-Humam, Fath al-Qadir; Haskafi, Durr al-Mukhtar]