Shaykh Muhammad ibn Saalih al-Uthaymeen rahimahullaah in his Majmoo` Fataawaa vol. 20 pge. 37-38 was asked the following question:
Q: What do you say regarding fasting a day after `Aashooraa, as that which is legislated is fasting a day before it. (So), is fasting a day after `Aashooraa established by way of an authentic narration from the Messenger of Allaah sallAllaahu `alaihi wa sallam?
A: (It has been reported) in the ‘Musnad’ of Imaam Ahmad: “Fast a day before it or a day after it. Differ from the Jews.”
[Reported by Ahmad 1/241, and Ibn Khuzaymah no. 2095, and Abdur-Razzaaq in his ‘Musannaf’ no. 7839, and by al-Haythamee in ‘Majmauz Zawaaid‘ 3/191; reported by Ahmad and al Bazzaar and in its chain of narration is Muhammad ibn Abee Laylaa – and there is some speech concerning him.]
And differing from the Jews is:
(a) Either by fasting the ninth day – as the Prophet sallAllaahu `alaihi wa sallam said: “If I live until the next year, I will certainly fast on the ninth day.” [Reported by Muslim no. 1134] Meaning: Along with the tenth day.
(b) Or by fasting a day after it; as the Jews used to single out the tenth day (with fasting).
So differing from them is achieved by fasting a day before it or a day after it.
And Ibnul-Qayyim rahimahullaah mentioned in ‘Zaadul Ma`aad‘ that fasting the day of `Aashooraa is of four types:
(1) That he fasts the tenth day alone.
(2) Or he fasts it [the tenth day] along with the ninth day.
(3) Or he fasts it [the tenth day] along with the eleventh day.
(4) Or he fasts all three days (i.e. the ninth, tenth, and eleventh together). And in fasting all three days there is an additional benefit – and it is that he achieves fasting three days from the month.