At every part of the night, the Messenger of Allah (may Allah's peace and blessings be upon him) prayed Witr: at its beginning, middle, and end. Finally he settled on performing Witr just before dawn
Authentic hadithعن عائشة رضي الله عنها قالت: «من كلِّ الليل أَوْتَرَ رسول الله صلى الله عليه وسلم : من أول الليل، وأوسطه، وآخره، وانتهى وِتْرُهُ إلى السَّحَرِ».
‘Ā'ishah (may Allah be pleased with her) reported: 'At every part of the night, the Messenger of Allah (may Allah's peace and blessings be upon him) prayed Witr: at its beginning, middle, and end. Finally he settled on performing Witr just before dawn.
Explanation
The Mother of the Believers ‘Ā'ishah (may Allah be pleased with her) mentions the time when the Prophet (may Allah's peace and blessings be upon him) used to pray Witr at night. He used to pray it at any time at night, without restricting himself to a certain time. Sometimes he would pray it at the beginning of the night after praying ‘Ishā'. Sometimes he would pray in the middle of the night after the first third of the night had passed. Sometimes he would pray in the last part of the night after two thirds had passed, even in the last hour of the night.
Source · Narrated by Bukhari & Muslim
From the Hadith Encyclopedia (hadeethenc.com).