Question: I often hear many imams—especially those who adhere to the Shafi‘i school—recite a fixed supplication after rising from bowing in the second rakʿah of the Fajr prayer. Does this supplication at that particular time have any basis in the Sunnah?
Answer: Yes. As you noted, the Shafiʿis perform qunūt in the Fajr prayer after they stand up from bowing in the second rakʿah, but the majority of scholars hold otherwise.
The majority do not consider qunūt in the Fajr prayer to be prescribed; rather, they limit qunūt in the obligatory prayers to times of calamity. When the Muslims are faced with a calamity, they perform qunūt, following the Prophet (peace and blessings be upon him), for he used to perform qunūt in such circumstances.
Outside of calamities, no sound narration shows that the Prophet (peace and blessings be upon him) consistently performed qunūt in the Fajr prayer. In fact, some Companions regarded it as an innovation and something newly introduced; when asked about it they said, “It is a new matter.” This proves that performing qunūt regularly in the Fajr prayer is a blameworthy innovation, for it is not part of the Prophet’s practice—his Sunnah was to perform qunūt in the obligatory prayers only when calamities struck.
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The regular Sunnah prayers
Question: What are the regular Sunnah prayers that are performed before and after the obligatory prayers?
Answer: The regular Sunnah prayers that accompany the obligatory prayers are those clarified in the hadith of ʿAbd Allah ibn ʿUmar (may Allah be pleased with them both). He said: “I memorised from the Messenger of Allah (peace and blessings be upon him) ten rakʿahs: two before Dhuhr, two after it, two after Maghrib in his house, two after ʿIshāʾ in his house, and two before—”