Is fasting on the first day of Muharram allowed? Are there any supporting Hadith?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Fasting the First day of Muharram is desirable just like fasting other days of this month. The Prophet said: “The best fasting after Ramadan is the fasting in the month of Muharram.”

An-Nawawi said: “Our scholars say: “Among the fasting that is desirable is the fasting of the four sacred months: Thul Qi’dah, Thul Hijjah, Muharram and Rajab, and the best among them is Muharram.” [End of quote]

Allah knows best.