Is the regular sunnah prayer to be offered before the obligatory prayer in Fajr prayer if the time for the obligatory prayer is limited?

If the situation is as the questioner described, then one should begin with the obligatory prayer (Fajr prayer) so that its time does not expire. If there is time remaining after the prayer, then one should perform the regular sunnah prayer (the two rak'ahs of Fajr). If there is no time remaining, then one should pray them after sunrise, based on the saying of the Messenger of Allah, peace and blessings be upon him: "Whoever did not pray the two rak'ahs of Fajr, let him pray them after the sun rises." A man once prayed the two rak'ahs of Fajr after the Fajr prayer, and the Prophet, peace and blessings be upon him, did not object to him.