The Prophet ﷺ said, "Whoever wishes may fast on the day of 'Ashura'."  

قَالَ النَّبِيُّ ﷺ يَوْمَ عَاشُورَاءَ إِنْ شَاءَ صَامَ  

That he heard Muawiya bin Abi Sufyan on the day of 'Ashura' during the year he performed the Hajj, saying on the pulpit, "O the people of Medina! Where are your Religious Scholars? I heard Allah's Apostle saying, 'This is the day of 'Ashura'. Allah has not enjoined its fasting on you but I am fasting it. You have the choice either to fast or not to fast (on this day).' "  

سَمِعْتُ رَسُولَ اللَّهِ ﷺ يَقُولُ هَذَا يَوْمُ عَاشُورَاءَ وَلَمْ يُكْتَبْ عَلَيْكُمْ صِيَامُهُ وَأَنَا صَائِمٌ فَمَنْ شَاءَ فَلْيَصُمْ وَمَنْ شَاءَ فَلْيُفْطِرْ  

This hadith is narrated on the authority of Hisham with the same chain of transmitters, but he made no mention in the first part of the hadith that the Messenger of Allah ﷺ used to observe fast, and said about the second part that he abandoned the (fast) of Ashura, and he who wished observed the fast and who wished otherwise abandoned it, and he did not hold it as the words of the Messenger of Allah ﷺ as mentioned in the narration transmitted by Jarir.  

وَكَانَ رَسُولُ اللَّهِ ﷺ يَصُومُهُ وَقَالَ فِي آخِرِ الْحَدِيثِ وَتَرَكَ عَاشُورَاءَ فَمَنْ شَاءَ صَامَهُ وَمَنْ شَاءَ تَرَكَهُ وَلَمْ يَجْعَلْهُ مِنْ قَوْلِ النَّبِيِّ ﷺ كَرِوَايَةِ جَرِيرٍ  

People of Medina, where are your scholars? I heard the Messenger of Allah ﷺ say on this very day: It is the day of 'Ashura. Allah has not made fasting on This day obligatory for you but I am fasting. He who likes to observe fast among you should do so, and he who likes not to observe it may not observe it.  

سَمِعْتُ رَسُولَ اللَّهِ ﷺ يَقُولُ لِهَذَا الْيَوْمِ هَذَا يَوْمُ عَاشُورَاءَ وَلَمْ يَكْتُبِ اللَّهُ عَلَيْكُمْ صِيَامَهُ وَأَنَا صَائِمٌ فَمَنْ أَحَبَّ مِنْكُمْ أَنْ يَصُومَ فَلْيَصُمْ وَمَنْ أَحَبَّ أَنْ يُفْطِرَ فَلْيُفْطِرْ  

Yahya related to me from Malik from Ibn Shihab that Humayd ibn Abd ar-Rahman ibn Awf heard Muawiya ibn Abi Sufyan say from the mimbar on the day of Ashura in the year in which he made the hajj, "People of Madina, where are your learned men? I heard the Messenger of Allah ﷺ say about this day, 'This is the day of Ashura, and fasting it has not been prescribed for you. I am fasting it, and whoever of you wants to fast it can do so, and whoever does not want to, does not have to.' "  

سَمِعْتُ رَسُولَ اللَّهِ ﷺ يَقُولُ لِهَذَا الْيَوْمِ هَذَا يَوْمُ عَاشُورَاءَ وَلَمْ يُكْتَبْ عَلَيْكُمْ صِيَامُهُ وَأَنَا صَائِمٌ فَمَنْ شَاءَ فَلْيَصُمْ وَمَنْ شَاءَ فَلْيُفْطِرْ  

[Machine] Moawiya gave a speech in Medina during a visit he made on the day of Ashura. He asked, "Where are your scholars, O people of Medina? I heard the Messenger of Allah ﷺ say, 'This is the day of Ashura, and it is not obligatory for you to fast on it, but I am fasting. Whoever wants to fast may do so.'"  

أَنَّ مُعَاوِيَةَ خَطَبَ بِالْمَدِينَةَ فِي قَدْمَةٍ قَدِمَهَا يَوْمَ عَاشُورَاءَ فَقَالَ أَيْنَ عُلَمَاؤُكُمْ يَا أَهْلَ الْمَدِينَةِ سَمِعْتُ رَسُولَ اللَّهِ ﷺ يَقُولُ «هَذَا يَوْمُ عَاشُورَاءَ وَلَمْ يُكْتَبْ عَلَيْكُمْ صِيَامُهُ وَأَنَا صَائِمٌ فَمَنْ أَحَبَّ أَنْ يَصُومَ فَلْيَصُمْ»