Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) narrates that the Messenger of Allah (peace and blessings be upon him) came to Madinah and saw that the Jews of Madinah fasted on the day of Ashura. The Messenger of Allah (peace and blessings be upon him) asked them: "What is this day on which you fast?" They said: This is a great day on which Allah Almighty saved Musa (peace be upon him) and the people of Musa from Pharaoh and drowned Pharaoh and the people of Pharaoh, so Musa (peace be upon him) fasted on it out of gratitude, and we (also) fast on it. The Messenger of Allah (peace and blessings be upon him) said: "We have a greater right to Musa (peace be upon him) and are closer to him than you." So the Messenger of Allah (peace and blessings be upon him) fasted on it himself and ordered that it be fasted.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8397
Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) narrates: I never saw the Messenger of Allah (peace and blessings be upon him) seeking out the fast of any day, preferring it over other fasts, except this day, that is, the day of Ashura, and the month of Ramadan.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8398
Abu Qatadah (may Allah be pleased with him) narrates that a Bedouin asked the Messenger of Allah (peace and blessings be upon him) about his fasting, and he (peace and blessings be upon him) became angry, and the anger was showing on his (peace and blessings be upon him) face. Then Umar bin al-Khattab (may Allah be pleased with him) stood up and began to say: 'Radina billahi rabban wa bil-islami dinan wa bi-Muhammadin nabiyya' "We are pleased with Allah as Lord, with Islam as religion, and with you (peace and blessings be upon him) as Prophet. I seek refuge in Allah from the anger of Allah and of the Messenger." Umar (may Allah be pleased with him) kept repeating this until he (peace and blessings be upon him) became calm. Then he said: O Messenger of Allah (peace and blessings be upon him)! What ruling do you give about a man who fasts the whole year? The Messenger of Allah (peace and blessings be upon him) said: "He has neither fasted nor broken his fast." O Messenger of Allah (peace and blessings be upon him)! What is the ruling about one who fasts two days and breaks his fast for one day? He said: "Who has the strength for that?" Then he said: What about one who breaks his fast for two days and fasts one day? He (peace and blessings be upon him) said: "I wish that I had been given the strength for that." Then he said: O Messenger of Allah (peace and blessings be upon him)! What do you say about fasting on Monday? He (peace and blessings be upon him) said: "That is the day on which I was born and on which the Shari'ah was revealed to me." He said: O Messenger of Allah (peace and blessings be upon him)! What do you say about a person who fasts one day and breaks his fast one day? He (peace and blessings be upon him) said: "That is the fast of my brother Dawud." Then he said: O Messenger of Allah (peace and blessings be upon him)! What do you (peace and blessings be upon him) say about fasting on the day of Ashura? He (peace and blessings be upon him) said: "I hope from Allah that He will forgive the sins of one year." Then he said: O Messenger of Allah (peace and blessings be upon him)! What do you (peace and blessings be upon him) say about a person who fasts on the Day of Arafah? He (peace and blessings be upon him) said: "I hope that Allah Almighty will forgive the sins of the previous year and the sins of the coming year."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8399
Aswad bin Yazid (may Allah have mercy on him) narrates: I have not seen anyone who ordered the fasting of the day of Ashura more than Ali and Abu Musa (may Allah be pleased with them both).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8400