Recently I have read a post which states that it is not right to fast on 10th of Muharram because on that day the army of yazid have fasted as a mark of their victory. Also some say those who fast on this day will see hell close to them and my sis had told me that she has read a post which states that Imam Khamenei also state it as something wrongful. So is it true or not?

We do not fast on Ashura rather we abstain from food and drink till after Asr salat without the intention of fasting. This is recommended.