Muhammad reported on the authority of some of his teachers that Ubayy b. Ka'b led them in prayer during Ramadan. He used to recite the supplication (in the witr) during the second half of Ramadan. (Using translation from Abū Dāʾūd 1428)   

أَنَّ أُبَيَّ بْنَ كَعْبٍ أَمَّهُمْ يَعْنِي فِي رَمَضَانَ وَكَانَ يَقْنُتُ فِي النِّصْفِ الْأَخِيرِ مِنْ رَمَضَانَ  

[Machine] Umar ibn al-Khattab gathered the people around Ubay ibn Ka'b and prayed with them for twenty nights. He did not lead them in prayer except for the remaining half. When the last ten nights came, he was absent and prayed in his house. They would say, "Ubay has stayed."  

أَنَّ عُمَرَ بْنَ الْخَطَّابِ ؓ جَمَعَ النَّاسَ عَلَى أُبَيِّ بْنِ كَعْبٍ فَكَانَ يُصَلِّي بِهِمْ عِشْرِينَ لَيْلَةً وَلَا يَقْنُتُ بِهِمْ إِلَّا فِي النِّصْفِ الْبَاقِي فَإِذَا كَانَتِ الْعَشْرُ الْأَوَاخِرُ تَخَلَّفَ فَصَلَّى فِي بَيْتِهِ فَكَانُوا يَقُولُونَ أَبَقَ أُبَيٌّ  

[Machine] He used to observe the last half of Ramadan devoutly.  

أَنَّهُ كَانَ يَقْنُتُ فِي النِّصْفِ الْأَخِيرِ مِنْ رَمَضَانَ  

[Machine] Some of them devoted themselves to themselves, then their father Halima Muadh Al-Qari' became their mentor.  

بَعْضُهُمْ قَدْ تَفَرَّغَ لِنَفْسِهِ ثُمَّ أَمَّهُمْ أَبُو حَلِيمَةَ مُعَاذٌ الْقَارِيُّ فَكَانَ يَقْنُتُ  

[Machine] That Ibn Umar used to not perform the Witr prayer except during the second half of Ramadan.  

أَنَّ ابْنَ عُمَرَ كَانَ لَا يَقْنُتُ فِي الْوِتْرِ إِلَّا فِي النِّصْفِ مِنْ رَمَضَانَ  

[Machine] Ibn Sirin disliked performing the Qunut (supplication) during Witr prayer except during the last half of Ramadan.  

كَانَ ابْنُ سِيرِينَ يَكْرَهُ الْقُنُوتَ فِي الْوِتْرِ إِلَّا فِي النِّصْفِ الْأَوَاخِرِ مِنْ رَمَضَانَ  

الْقُنُوتُ فِي النِّصْفِ الْأَوَاخِرِ مِنْ رَمَضَانَ  

[Machine] As for the mosques of the congregation, they pray from the first of the month until the end, and as for the people of the city, they pray in the remaining half until its end. A hadith has been narrated about it, but it is weak, and its chain of narration is not valid.  

أَمَّا مَسَاجِدُ الْجَمَاعَةِ فَيَقْنُتُونَ مِنْ أَوَّلِ الشَّهْرِ إِلَى آخِرِهِ وَأَمَّا أَهْلُ الْمَدِينَةِ فَإِنَّهُمْ يَقْنُتُونَ فِي النِّصْفِ الْبَاقِي إِلَى انْسِلَاخِهِ وَقَدْ رُوِيَ فِيهِ حَدِيثٌ مُسْنَدٌ إِلَّا أَنَّهُ ضَعِيفٌ لَا يَصِحُّ إِسْنَادُهُ  

[Machine] The Messenger of Allah ﷺ used to observe voluntary worship during the second half of Ramadan until its end. Abu Ahmad Abu Atika Tarif ibn Salman, also known as Ibn Suleiman, a narrator of weak hadith, reported that he heard Ibn Hammad mentioning this narration from Al-Bukhari.  

كَانَ رَسُولُ اللهِ ﷺ يَقْنُتُ فِي النِّصْفِ مِنْ رَمَضَانَ إِلَى آخِرِهِ قَالَ أَبُو أَحْمَدَ أَبُو عَاتِكَةَ طَرِيفُ بْنُ سَلْمَانَ وَيُقَالُ ابْنُ سُلَيْمَانَ مُنْكَرُ الْحَدِيثِ سَمِعْتُ ابْنَ حَمَّادٍ يَذْكُرُهُ عَنِ الْبُخَارِيِّ