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

قَالَ النَّبِيُّ ﷺ يَوْمَ عَاشُورَاءَ إِنْ شَاءَ صَامَ  

Messenger of Allah ﷺ ordered (the Muslims) to fast on the day of 'Ashura', and when fasting in the month of Ramadan was prescribed, it became optional for one to fast on that day ('Ashura') or not.  

كَانَ رَسُولُ اللَّهِ ﷺ أَمَرَ بِصِيَامِ يَوْمِ عَاشُورَاءَ فَلَمَّا فُرِضَ رَمَضَانُ كَانَ مَنْ شَاءَ صَامَ وَمَنْ شَاءَ أَفْطَرَ  

Quraish used to fast on the day of 'Ashura' in the Pre-Islamic period, and Messenger of Allah ﷺ too, used to fast on that day. When he came to Medina, he fasted on that day and ordered others to fast, too. Later when the fasting of the month of Ramadan was prescribed, he gave up fasting on the day of 'Ashura' and it became optional for one to fast on it or not.  

كَانَ يَوْمُ عَاشُورَاءَ تَصُومُهُ قُرَيْشٌ فِي الْجَاهِلِيَّةِ وَكَانَ رَسُولُ اللَّهِ ﷺ يَصُومُهُ فَلَمَّا قَدِمَ الْمَدِينَةَ صَامَهُ وَأَمَرَ بِصِيَامِهِ فَلَمَّا فُرِضَ رَمَضَانُ تَرَكَ يَوْمَ عَاشُورَاءَ فَمَنْ شَاءَ صَامَهُ وَمَنْ شَاءَ تَرَكَهُ  

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  

The Prophet ﷺ came to Medina and saw the Jews fasting on the day of Ashura. He asked them about that. They replied, "This is a good day, the day on which Allah rescued Bani Israel from their enemy. So, Moses fasted this day." The Prophet ﷺ said, "We have more claim over Moses than you." So, the Prophet fasted on that day and ordered (the Muslims) to fast (on that day).  

قَدِمَ النَّبِيُّ ﷺ الْمَدِينَةَ فَرَأَى الْيَهُودَ تَصُومُ يَوْمَ عَاشُورَاءَ فَقَالَ مَا هَذَا قَالُوا هَذَا يَوْمٌ صَالِحٌ هَذَا يَوْمٌ نَجَّى اللَّهُ بَنِي إِسْرَائِيلَ مِنْ عَدُوِّهِمْ فَصَامَهُ مُوسَى قَالَ فَأَنَا أَحَقُّ بِمُوسَى مِنْكُمْ فَصَامَهُ وَأَمَرَ بِصِيَامِهِ  

The day of 'Ashura' was considered as ʿId day by the Jews. So the Prophet ﷺ ordered, "I recommend you (Muslims) to fast on this day."  

كَانَ يَوْمُ عَاشُورَاءَ تَعُدُّهُ الْيَهُودُ عِيدًا قَالَ النَّبِيُّ ﷺ فَصُومُوهُ أَنْتُمْ  

I never saw the Prophet ﷺ seeking to fast on a day that he favored more than another except this day, the day of 'Ashura', and this month, meaning the month of Ramadan.  

مَا رَأَيْتُ النَّبِيَّ ﷺ يَتَحَرَّى صِيَامَ يَوْمٍ فَضَّلَهُ عَلَى غَيْرِهِ إِلاَّ هَذَا الْيَوْمَ يَوْمَ عَاشُورَاءَ وَهَذَا الشَّهْرَ يَعْنِي شَهْرَ رَمَضَانَ  

The Prophet ﷺ ordered a man from the tribe of Bani Aslam to announce amongst the people that whoever had eaten should fast the rest of the day, and whoever had not eaten should continue his fast, as that day was the day of 'Ashura' .  

أَمَرَ النَّبِيُّ ﷺ رَجُلاً مِنْ أَسْلَمَ أَنْ أَذِّنْ فِي النَّاسِ أَنَّ مَنْ كَانَ أَكَلَ فَلْيَصُمْ بَقِيَّةَ يَوْمِهِ وَمَنْ لَمْ يَكُنْ أَكَلَ فَلْيَصُمْ فَإِنَّ الْيَوْمَ يَوْمُ عَاشُورَاءَ