Al-Abbas bin al-Walid bin Mazyad narrates from his father that al-Awza'i (may Allah have mercy on him) was asked about the qunut in the month of Ramadan. He said: In the congregational mosques the qunut was recited from the beginning of the month to its end, but the people of Madinah would recite the qunut in the last half.
A hadith with a connected chain has been narrated about this, but it is weak; its chain is not sound.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 4636