Hadith on Ashura: This is the day Moses fasted to thank Allah for saving his people
Ibn Abbas reported: The Messenger of Allah, peace and blessings be upon him, came to Medina and he found the Jews fasting the day of Ashura. The Prophet said, “What is this day you are fasting?” They said, “This is a great day in which Allah saved Moses and his people, and He drowned Pharaoh and his people. Moses fasted on it due to gratitude, so we also fast on it.” The Prophet said, “We have more right to it and we are closer to Moses than you.” The Prophet fasted the day of Ashura and he commanded fasting on it.
Source: Ṣaḥīḥ al-Bukhārī 3216, Ṣaḥīḥ Muslim 1130
Hadith on Fasting: Sins are erased by fasting on the day of Arafat and Ashura
Abu Qatadah reported: The Prophet, peace and blessings be upon him, was asked about fasting the day of ‘Arafāt. The Prophet said, “It will expiate the sins of the previous and upcoming years.” Then he was asked about fasting the day of ‘Ashūrā. The Prophet said, “It will expiate the sins of the year.”
Source: Ṣaḥīḥ Muslim 1162
Grade: Sahih (authentic) according to Muslim