Messenger of Allah ﷺ used to practice Iʿtikaf in the last ten days of the month of Ramadan.  

كَانَ رَسُولُ اللَّهِ ﷺ يَعْتَكِفُ الْعَشْرَ الأَوَاخِرَ مِنْ رَمَضَانَ  

(the wife of the Prophet) The Prophet ﷺ used to practice Iʿtikaf in the last ten days of Ramadan till he died and then his wives used to practice Iʿtikaf after him.  

زَوْجِ النَّبِيِّ ﷺ أَنَّ النَّبِيَّ ﷺ كَانَ يَعْتَكِفُ الْعَشْرَ الأَوَاخِرَ مِنْ رَمَضَانَ حَتَّى تَوَفَّاهُ اللَّهُ ثُمَّ اعْتَكَفَ أَزْوَاجُهُ مِنْ بَعْدِهِ  

Messenger of Allah ﷺ used to practice Iʿtikaf in the middle ten days of Ramadan and once he stayed in Iʿtikaf till the night of the twenty-first and it was the night in the morning of which he used to come out of his Iʿtikaf. The Prophet ﷺ said, "Whoever was in Iʿtikaf with me should stay in Iʿtikaf for the last ten days, for I was informed (of the date) of the Night (of Qadr) but I have been caused to forget it. (In the dream) I saw myself prostrating in mud and water in the morning of that night. So, look for it in the last ten nights and in the odd ones of them." It rained that night and the roof of the mosque dribbled as it was made of leaf stalks of date-palms. I saw with my own eyes the mark of mud and water on the forehead of the Prophet (i.e. in the morning of the twenty-first).  

عَنْ أَبِي سَعِيدٍ الْخُدْرِيِّ ؓ أَنَّ رَسُولَ اللَّهِ ﷺ كَانَ يَعْتَكِفُ فِي الْعَشْرِ الأَوْسَطِ مِنْ رَمَضَانَ فَاعْتَكَفَ عَامًا حَتَّى إِذَا كَانَ لَيْلَةَ إِحْدَى وَعِشْرِينَ وَهِيَ اللَّيْلَةُ الَّتِي يَخْرُجُ مِنْ صَبِيحَتِهَا مِنِ اعْتِكَافِهِ قَالَ مَنْ كَانَ اعْتَكَفَ مَعِي فَلْيَعْتَكِفِ الْعَشْرَ الأَوَاخِرَ وَقَدْ أُرِيتُ هَذِهِ اللَّيْلَةَ ثُمَّ أُنْسِيتُهَا وَقَدْ رَأَيْتُنِي أَسْجُدُ فِي مَاءٍ وَطِينٍ مِنْ صَبِيحَتِهَا فَالْتَمِسُوهَا فِي الْعَشْرِ الأَوَاخِرِ وَالْتَمِسُوهَا فِي كُلِّ وِتْرٍ فَمَطَرَتِ السَّمَاءُ تِلْكَ اللَّيْلَةَ وَكَانَ الْمَسْجِدُ عَلَى عَرِيشٍ فَوَكَفَ الْمَسْجِدُ فَبَصُرَتْ عَيْنَاىَ رَسُولَ اللَّهِ ﷺ عَلَى جَبْهَتِهِ أَثَرُ الْمَاءِ وَالطِّينِ مِنْ صُبْحِ إِحْدَى وَعِشْرِينَ