You are not allowed to claim that at all since the child does not live with you*. But the father may count what you paid in claiming the dependent care credit for himself.
* It's not relevant this year, but you can not claim the day care credit, even when you are claiming the dependent, if the child doesn't live with you.
This may be helpful in your
negotiations with the ex:
There is a
special rule in the case of divorced & separated (including never married) parents.
When the non-custodial parent is claiming the child as a
dependent/exemption/child tax credit; the custodial parent is still allowed to
claim the same child for Earned Income Credit, Head of Household filing status,
and day care credit. This "splitting of the child" is not available
to parents who lived together at any time during the last 6 months of the year;
then only one of you can claim the child for any tax reasons. The tax benefits
may not be split in any other manner.
Note in particular
that the non-custodial parent can never claim the Earned Income Credit, Head of
Household filing status or the day care credit, based on that child,
even when the custodial parent has released the exemption to him.
So,
it's good idea to let the other parent know that you will be claiming those
items, as many first time divorced parents are not aware of this rule and may
try to claim those items, which will cause the IRS to send out letters.
Ref: http://www.irs.gov/publications/p17/ch03.html#en_US_2014_publink1000170897
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of divorced or separated parents (or parents who live apart)"
