Answer
(Fatwa: 932/528/D=1432)
The sunnah of Fajr carries high importance. If one hopes that he would join the imam in last Qa’da, he should join the jama’ah after offering sunnah. If you are in the mosque you should offer sunnah in the outer part of the mosque or in verandah or behind any column. And if you fear that you would miss last Qa’da in case you offer sunnah then you should join the jama’ah. In this case, neither there is qaza of the sunnah nor it is lawful to offer sunnah after the fardh salah. However, if one offers it with the intention of nafl after 15 minutes of the sunrise then it is alright.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband