What is the virtue of fasting on the first of Muharram?

There is no fixed text regarding the specific virtue of fasting the first day of Muharram. However, it is prescribed to fast it due to the general evidence that encourages increasing fasting in Muharram, and because the Prophet (peace and blessings be upon him) used to fast three days at the beginning of every month. So, whoever fasts it with this intention, it is good. As for believing in a special virtue for it, there is no evidence for that.