Is it correct to say on yesterday or on tomorrow?

No. In English we may say that something happened (or will happen) "on" a particular day or date (eg: Tuesday, or 15th March) but we do not say "on" yesterday and tomorrow. If something happened (or will happen) during a certain month but not on a specific date we may say "in" Eg: I am going shopping on Friday. My birthday was on the 17th June. I went swimming yesterday. I will visit a friend tomorrow. I am going to have a holiday in December.