Is it permissible to recite Al-Fatihah twice in a single rak'ah of a fard prayer, with the second recitation intended as a supplication?

Repeating Al-Fatiha in a single rak'ah does not invalidate the prayer, but it is not permissible according to many scholars, and it is forbidden if done intentionally. One must perform the prostration of forgetfulness (sujud as-sahw) for it, as it is among the prayer's obligations. An exception to this is repeating it due to doubt about having recited it, or having omitted a verse from it, or to achieve the Sunnah of audibility or silence.