What is the ruling of fasting on a day thinking that it is the tenth of Muharram according to the calendars found in bookshops but, in the middle of the day, I discovered that it is the eleventh day of Muharram?

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.

You should have checked and asked about the time when the moon was sighted in a Sharee’ah-approved manner. You should not have depended only on the calendar that may have been right or wrong. What counts is a Sharee’ah-approved moon sighting.

If you did not fast on the tenth day thinking that it is the ninth day, then it is an act of the Sunnah that you missed and, due to this, you also missed the day of ‘Aashooraa’ because it is the tenth day of Muharram. You are rewarded, Allaah Willing, for your intention and sincere desire to fast on the day of ‘Aashooraa’. The Prophet, sallallaahu ‘alayhi wa sallam, said: "When a slave falls ill or travels, then he will receive a reward similar to that which he gets for good deeds he used to perform  at home while in good health." [Al-Bukhari]

You are also rewarded for your voluntary fasting on the eleventh day. Allaah The Almighty never Wastes the reward of he who does good deeds. From here on, you should seek (a confirmation of) the moon being sighted to avoid making such a mistake.

Allaah Knows best.