Q: 10th of muharam is an important day. Can we fast only on this day? (text)
A: It is against the sunnah to fast only on the 10th day of Muharram. It will be makrooh to do so. If one chooses to fast, it should be on the 9th and 10th or on the 10th or 11th. saheeh Muslim #1162

Allah Certainly Knows Best.