Are you asking about 2016 or 2017?
If the 3 months the father lived with you included all the time in December since the child was born; either one of you can claim the child for 2016. If you cannot agree on who will claim the child, the parent with the highest income has first right.
For 2017, you have the higher right since the child lived you more than with the father.
You can allow the father to claim the child, instead of you, but he cannot claim the Earned Income Credit (EIC), because he did not reside with the child enough to qualify for EIC; so it's unlikely he can "get more" (but still possible, depending how much income you each have).
