“The Messenger of Allah (ﷺ) said: ‘The best of fasting after Ramadan is fasting Allah’s month of Muharram.'” (Muslim).
The Prophet (ﷺ) encourages us to take up a fast during Muharram, on the 9th and 10th (or 10th and 11th) days of Ashura. That is Thursday and Friday or Friday and Saturday.
The Prophet himself fasted on the 10th, the day of Ashura, and had fully intended to take up a fast the following year on the 9th, but he passed away before he could.
