Is it narrated that the Prophet (peace be upon him) remained silent after the recitation of Al-Fatiha and a surah in the second rak'ah of the Fajr prayer, and is it permissible to supplicate at this time, or must one remain silent?

The silent Qunut performed by the Imam in the second rak'ah of the Fajr prayer is the madhhab (definition) of the Malikis and one view among the Shafi'is. Scholars have differed regarding the ruling on Qunut in Fajr prayer. It is well-known among the Malikis and Shafi'is that it is prescribed, while the Hanafis and Hanbalis hold that it is not prescribed except in times of calamity (nawazil). The more preponderant view is not to perform Qunut except in times of calamity. However, there is no harm in praying behind one who performs Qunut and saying Ameen to his supplication, whether the Imam vocalizes or performs it silently. In the case of silent Qunut, the worshipper should supplicate to himself.