The Messenger of Allah ﷺ performed witr at every part of the night, and his witr eventually settled at the time just before dawn.
حدثنا أبو معاوية حدثنا الأعمش عن مسلم عن مسروق عن عائشة وابن جعفر حدثنا شعبة عن سليمان قال سمعت أبا الضحى عن مسروق
من كل الليل قد أوتر رسول الله ﷺ فانتهى وتره إلى السحر
Its isnad is sahih. Muslim reported it, 1/512, no. 745, in the book of travelers, and Abu Dawud, 2/66, no. 1435, and Tirmidhi, 2/319, no. 459, who said it is hasan sahih, and Darimi, 1/450, no. 1587, all of them in the book of prayer, in the chapter on what has been said about Witr.