Ibn Sirin (may Allah have mercy on him) narrates from some of his companions that Ubayy bin Ka'b (may Allah be pleased with him) led them in prayer in Ramadan, and he would recite the qunut in the last fifteen days of Ramadan.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 4629
Al-Hasan (may Allah have mercy on him) says that Sayyiduna Umar bin al-Khattab (may Allah be pleased with him) gathered the people behind Sayyiduna Ubayy bin Ka'b (may Allah be pleased with him). He would lead them in tarawih for twenty nights, and would recite the qunut only in the remaining half (the last fifteen days). When the last ten days came, Sayyiduna Ubayy bin Ka'b (may Allah be pleased with him) would pray in his house, and the people would say: Ubayy has run away.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 4630
Al-Harith (may Allah have mercy on him) says that Sayyiduna Ali (may Allah be pleased with him) used to recite the qunut in the last fifteen days of Ramadan.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 4631
Al-Hasan (may Allah have mercy on him) says that Sayyiduna Ali (may Allah be pleased with him) led us in prayer for twenty nights in the time of Sayyiduna Uthman bin Affan (may Allah be pleased with him), then he stopped. Some said: He has set aside time for himself. Then Abu Halimah Mu'adh (may Allah have mercy on him) led them, and he would recite the qunut.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 4632
Sallam bin Miskin (may Allah have mercy on him) says that Ibn Sirin (may Allah have mercy on him) disliked the qunut in witr, but considered it permissible after the middle of Ramadan.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 4634
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
Sayyiduna Anas (may Allah be pleased with him) says that the Messenger of Allah (peace and blessings be upon him) used to recite the qunut after the middle of Ramadan.
Abu Ahmad (Ibn Adi) said: Abu Atikah Tarif bin Salman (also called Ibn Sulayman) is munkar al-hadith (his narrations are rejected); I heard Ibn Hammad mention this from al-Bukhari.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 4637