Who can claim the child if the child lives with the mother and the father lives somewhere else and has only lived with the child for 3 months

[babybear_1994]

our child was born in December 2016, I claimed him on taxes. his father lived with us for 3 months before we broke up. he says he can get more for the child even though he hasn't filed taxes in 3 years, & the child doesn't live with him, & he only seen him 3 times since we broke up.  

[Hal_Al]

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).

[babybear_1994]

for 2017. he only lived with us for 2 weeks in December.

[babybear_1994]

I claimed the child in 2016

[SweetieJean]

"for 2017. he only lived with us for 2 weeks in December."
It's not December yet.

[Critter]

The parent with whom the child lives more than half the year (184 or more 184 nights for 2016) is automatically entitled to claim the child as a dependent. This is the custodial parent. (IRS determines custody based on where the child lives, not any court order or agreement.)  The non-custodial parent is not entitled to claim anything.

However, the custodial parent can sign a release (form 8332) allowing the non-custodial parent to claim the child as a dependent.  You can download this form from the IRS web site.  The custodial parent signs it and gives it to the non-custodial parent and the non-custodial parent mails it to the IRS after e-filing the rest of their tax return.  In this case, the non-custodial parent can claim the dependent exemption and the child tax credit.  The non-custodial parent can never claim earned income credit, the dependent care credit (day care credit) or use the child to qualify for head of household status.  Those benefits always stay with the custodial parent.