All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
As long as you intended to observe fasting on the day of ‘Aashooraa’ and then sickness prevented you from doing so, you will get the reward of fasting on this day, if Allaah wills. The Prophet, sallallaahu ‘alayhi wa sallam, said: "When a slave suffers from illness or sets out on a journey, he is credited with the equal of whatever good deeds he used to do when he was healthy or at home." [Al-Bukhari]
Making up for the day of ‘Aashooraa’ is recommended according to some scholars, such as the Shaafi‘i scholars who held that it is recommended to make up for confirmed voluntary fasting days when missed. Shams Ad-Deen Ar-Ramli, a Shaafi‘i scholar, said, “A Muslim who misses some days that he is used to fasting on, such as Mondays, it is not an act of Sunnah to make up for them due to lack of the fundamental reason, as stated earlier in the Fatwa given by my late father . However, this is contested by his previous Fatwa which permitted making up for the six days missed in Shawwaal in the month of Thul-Qa‘dah with the justification that it is recommended to make up for the confirmed voluntary fasting days when missed. Thus, this is the sounder opinion.”
Allaah Knows best.