Intended to Fast `Ashura but Didn’t Fast It: What to Do?
Question

My question is about the Day of `Ashura. I intended to fast the three days, and I fasted on the ninth day [of al-Muharram], but by mistake I did not fast on the tenth day, and I am going to fast the eleventh day. I know that the fast of `Ashura [the tenth day] will not be counted for me, but I still want to attain its reward and expiation for the year. How can I compensate for this day and seek the reward, by Allah’s leave?
Praise be to Allah.Fasting `Ashura
Some of the jurists regarded it as recommended to fast the day of `Ashura and to fast the day before it and the day after it, and some of the scholars regarded that as the most perfect way of doing it. 
Ibn al-Qayyim (may Allah have mercy on him) said:
“The ways of fasting `Ashura are three, the most perfect of which is to fast one day before it and one day after it. The next best is to fast the ninth and tenth days, which is what is mentioned in most of the hadiths. The next best thing is to fast on the tenth day only.” (Zad al-Ma’ad (2/76).
Scenarios of Intending to fast `Ashura but not fasting it
If a person decides to fast the day of `Ashura then does not fast it, one of the following scenarios must apply:

Either he deliberately did not do it, in which case it will not be recorded that he fasted `Ashura and he will not attain the virtue thereof, because he did not fast that day;
or he did not do it because he forgot, although he intended to fast it, in which case we hope that he will have the reward thereof, in sha Allah;
or he did not do it because he was sick, although he usually fasted it before that, or he had decided to fast it this time, but sickness prevented him from doing so, in which case we hope that he will also have the reward for fasting it, because he had an excuse, because of the report narrated by al-Bukhari (2996) from Abu Musa (may Allah be pleased with him) who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “If a person falls sick or travels, (a reward) will be recorded for him like that of the deeds that he used to do when he was not travelling and was in good health.”

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
“This hadith indicates that there will be recorded for him a reward like that which was recorded for him when he was in good health and was not travelling, because he intended to do it but was prevented from doing so by that excuse.” (Majmu‘ al-Fatawa, 23/236)
Ibn Baz (may Allah have mercy on him) was asked:
I am a man who fasts the day of ‘Arafah every year, and also `Ashura, but last year I forgot the day of `Ashura, and I broke the fast on that day because I forgot that it was the day of `Ashura. But I completed my fast, and I also fasted on the eleventh day (of Muharram). Is what I did correct?
He replied:
“With regard to `Ashura [sic – probably he meant al-Muharram], it is good to fast on any day throughout the month. If you fast whatever of it you are able to, then praise be to Allah, and we hope that you will have the reward for the day that you missed out on because you forgot, for you did not omit to do it deliberately; rather it was because you forgot, so you will have the reward for it, in sha Allah. Your fasting on the eleventh day is also good, because you missed the tenth day because you forgot, so you will have the reward for it, just as if you missed it because you were sick, then you got better on the eleventh day.”
Breaking `Ashura fast
With regard to your breaking the fast on the Day of `Ashura , even though you had intended to fast it, if you had an excuse, then we hope that you will have the reward, but if it was with no excuse, then you will not have any reward, because the reward is for one who does the deed or one who intends to do the deed, but is prevented from doing it because of some excuse. 
Al-Bukhari (4423) narrated from Anas ibn Malik (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) came back from the campaign to Tabuk, and when he grew close to Madinah he said: “In Madinah there are people who, whenever you travelled any distance or crossed any valley, were with you.” They said: O Messenger of Allah, even though they are in Madinah? He said: “Even though they are in Madinah, because they were kept there by excuses.”
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
“They intended to do that good deed that they had done previously, and wanted to do it, but they were unable to do it; thus they were of the same status as those who did it.” (Majmu‘ al-Fatawa, 10/441)
If you were negligent about fasting `Ashura, then let this negligence and missing out on the reward prompt you in the future to have a firm resolve to do good deeds and acts of obedience, and not to neglect that.
One way to make up for what you have missed out on of reward is to fast whatever you are able to of al-Muharram, the sacred month of Allah, because of its virtue. Muslim (1163) narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “The best fast after Ramadan is al-Muharram, the sacred month of Allah." 
With regard to expiation of sins, that may be attained by renewing and perfecting your repentance, and constantly asking Allah for forgiveness. 
Although fasting `Ashura expiates the sins of a year, and fasting ‘Arafah expiates the sins of two years, sincere repentance expiates all sins. 
For more, please see this answer: 21819 .
And Allah knows best.