Ibn Abbas (RA) was asked about observing of fast on the day of Ashura, whereupon he said: I do not know Allah's Messenger (ﷺ) singling out any day's fast and considering it more excellent than another, except this day (the day of Ashura) and this month, meaning the month of Ramadan.
´It was narrated from 'Ubaidullah that:` he heard Ibn 'Abbas, when he was asked about the fast of 'Ashura' say: "I do not know that the Prophet fasted any day because of its virtue, except this day" meaning the month of Ramadan and the day of Ashura.'
Hafiz Muhammad Ameen
Urdu marginal note: There is no doubt whatsoever regarding the virtue of the blessed month of Ramadan; after it, the Day of Ashura, that is, the tenth of Muharram al-Haram, is the most virtuous. Many significant events took place on this day.
Source: Sunan Nasa'i: Translation and Benefits by Shaykh Hafiz Muhammad Amin Hafizullah, Page: 2372
Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) narrates: To my knowledge, the Noble Prophet (peace and blessings be upon him) never fasted on any specific day with special care to attain its virtue except for this day. Sayyiduna Ibn Abbas (may Allah be pleased with them both) meant the day of Ashura, or this month. Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) meant the month of Ramadan.
Shaykh Muhammad Ibrahim bin Basheer
Benefit: From this hadith, it is understood that the fasts of Ramadan and Ashura (the ninth day of Muharram) possess great virtue. Apart from these, all other days are equal in terms of fasting. If someone wishes, they may observe the fast of Dawud (صوم داؤدی) — that is, fasting one day and breaking the fast the next — or they may keep the fasts of Ayyam al-Beedh (ایام بیض), which are the fasts on the 13th, 14th, and 15th of each lunar month.
Source: Musnad al-Humaydi: Commentary by Muhammad Ibrahim bin Bashir, Page: 490