Is the fast broken and a make-up required for one who intended to fast the twenty-second day of Ramadan, which was a Monday, then it became clear to him that it was a Sunday?

Your fast for that day is valid, and there is no need for a make-up fast. The error in calculation has no effect as long as you intended to fast the following day. If a person intends to fast a day and makes an error in describing it, such as believing it is Monday when it is actually Tuesday, their fast is valid.