I want to draw a DFA to accept a String containing even number of both A and B, but rejects the empty String(ε)
I have already drawn the DFA which accepts the above language, without rejecting the empty string.
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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.