Does being overcome by drowsiness during the Fajr prayer necessitate redoing it or making it up?

The prayer of the congregant is valid as long as he understands the prayer and follows the Imam, and this is the fundamental principle. If the congregant ascertains that he did not recite Al-Fatihah or the Tashahhud after the Imam, he should then perform it and then conclude with the salām. However, if he omitted Al-Fatihah in a rak'ah due to forgetfulness or ignorance, the Imam bears it on his behalf.