He intended to fast ‘Ashoora’, then he did not fast it; how can he make up what he missed out on of reward and virtue?

Firstly:

Some of the fuqaha’ regarded it
as mustahabb (recommended) to fast the day of ‘Ashoora’ 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 ‘Ashoora’
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 is to fast the tenth
day only.

End quote from Zaad al-Ma‘aad
(2/76).

See also the answer to question
no. 128423

Secondly:

If a person decides to fast the
day of ‘Ashoora’ 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 ‘Ashoora’ 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-Bukhaari (2996) from Abu Moosa (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.

End quote from Majmoo‘ al-Fataawa
(23/236)

Ibn Baaz (may Allah have mercy
on him) was asked:

I am a man who fasts the day of
‘Arafah every year, and also ‘Ashoora’, but last year I forgot the day of ‘Ashoora’,
and I broke the fast on that day because I forgot that it was the day of ‘Ashoora’.
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 ‘Ashoora’ [sic –
probably he meant 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.
End quote.

http://www.binbaz.org.sa/mat/13711

With regard to your breaking
the fast on the Day of ‘Ashoora’, 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, as al-Bukhaari (4423)
narrated from Anas ibn Maalik (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 Tabook, 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.

End quote from Majmoo‘ al-Fataawa
(10/441)

If you were negligent about
fasting ‘Ashoora’, then let this negligence and missing out on the reward
prompt you in the future to have 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
Muharram, the sacred month of Allah, because of its virtue, as 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 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 ‘Ashoora’
expiates the sins of a year, and fasting ‘Arafah expiates the sins of two
years, sincere repentance expiates all sins. 

For more information, please
see the answer to question no. 21819

And Allah knows best.