Is there a specific prayer or fast unique to the month of Muharram?

There is no obligatory or binding act of worship, such as a specific prayer or fast, prescribed for blessed days and nights. There are no authentic reports in reliable sources indicating the existence of a special voluntary prayer unique to the month of Muharram.

For those who have missed obligatory prayers, it is more appropriate to make up those prayers during blessed days and nights. Additionally, one should not neglect reading and understanding the Qur’an, benefiting from religious works, and engaging in remembrance of Allah and sending blessings upon the Prophet.

Fasting during the month of Muharram is considered recommended (mustahabb). One may fast at the beginning, end, or middle of this month—that is, on the 13th, 14th, and 15th days, or on the 9th and 10th, or the 10th and 11th days.

The Messenger of Allah (peace and blessings be upon him) said: “After the fast of Ramadan, the most virtuous fast is that which is observed in Allah’s month, Muharram. And the most virtuous prayer after the obligatory ones is the night prayer.” (Muslim, Sawm, 202-203 [1163])

The 10th day of Muharram is called the Day of Ashura. The Messenger of Allah (peace and blessings be upon him) said: “I hope that fasting on the Day of Ashura will atone for the (minor) sins of the previous year.” (Muslim, Sawm, 196-197 [1162]), thus recommending his community to fast on this day. Regarding fasting on the Day of Ashura, Ibn Abbas (may Allah be pleased with him) narrates: “When the Messenger of Allah (peace and blessings be upon him) came to Medina, he saw that the Jews were fasting on the Day of Ashura. He asked them, ‘What is this (why are you fasting)?’ They replied, ‘This is a righteous day. On this day, Allah saved the Children of Israel from their enemy, and Moses fasted on this day (in gratitude).’ The Messenger of Allah (peace and blessings be upon him) said, ‘I am closer to Moses than you are,’ so he fasted on that day and recommended the Muslims to do so as well.” (Bukhari, Sawm, 69 [2004]; Muslim, Sawm, 127-128 [1130])

During the time of the Prophet (peace and blessings be upon him), the Jews would fast only on the 10th day (Ashura) of Muharram. To distinguish the Muslim practice from theirs, the Prophet (peace and blessings be upon him) recommended fasting an additional day either before or after. In some reports, he recommended fasting three days by adding both the day before and the day after. (Bazzar, al-Musnad, 11/399 [5238]; Bayhaqi, as-Sunan al-Kubra, 4/475 [8406]) Therefore, when fasting on the Day of Ashura, it is important not to fast only on that day. One may fast two days by adding either the previous or following day, or three days by including both.

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu