To read Fajr sunnah after the jamaat has started
Answer:
Saaiduna Abu Hurairah 
narrates that the Prophet of Allah 
said; “Do not leave the two (sunnah) rakaat of Fajr, even if you are being attacked by a cavalry.” (Sunan Abi Dawud p.186 v.1)
Imam Shafi 
and Imam Ahmad Bin Hanbal are of the view that if a person arrives at the masjid at such a time where the congregation of the Fajr prayer has started he should join the congregation and perform the two rakats of Fajr sunnah after the fardh salah either before sunrise or after that. On the other hand according to Imam Malik if one expects to find at least one rakaat or the congregation he will be allowed to pray the sunnah of Fajr. (Dars Tirmizi p.186 v.2) This is also the opinion of Imam Abu Hanifah (See Hidayah p.152 v.1). However, another opinion in the Hanafi Fiqh is that if one expects to find the salam of the fardh prayer then one can commence the Fajr sunnah preferably away from the congregation like at the back of the mosque or in another room.
Some additional rulings to keep in mind with regards to the Fajr sunnah.
- If one has missed his fardh and he is doing qadha of the salah before zawaal of that day then he should also do qadha of the Fajr sunnah along with the fardh. (Fatawa Mahmoodiyah p.54 v.13)
- If one has read the fardh of Fajr already without reading the sunnah, then there is no qadha of the sunnah afterwards. (Fatawa Darul Uloom Deoband p.215 v.4)
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham.