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).
Sahih al-Bukhari Book 30, Hadith 109
← Previous Hadith 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).' "

Sahih al-Bukhari Book 30, Hadith 108 Next Hadith → The day of 'Ashura' was considered as `Id day by the Jews. So the Prophet (ﷺ) ordered, "I recommend you (Muslims) to fast on this day."

Sahih al-Bukhari Book 30, Hadith 110