1. Well, both your parents had equal half share in the proeprty.
2.So on the death of your father his half share further devolves upon you and your mother.
3.So presently you are already 25% share holder in the flat while your mother is 75% shareholder.
4.So by law of inheritance you are already joint owner of the flat and hence no additional measure is to be taken to make you its joint owner..
5.Now the falt can be mutated both in the name of yours and your mother.