DFA to accept a String containing even number of both A and B, but rejects empty String
I'm going to assume that your DFA has 4 states with the start state also being the singular accepting state.
Add a new (non-accepting) state where the outgoing transitions are a copy from your existing accepting start state. Make that new state the start state.
If my assumption about your existing DFA is correct then this way you should not be able to get into an accepting state with the empty string.