Deductions & credits

If the non-custodial parent (or anyone else) claims your child and files first, you will be unable to e-file your return claiming the child.  If your e-file is rejected due to duplicate use of your child's SSN, you have to file by mail.  Then the IRS processes your return and later they sort out the duplicate use of the SSN.  If someone who should not have claimed the child did so and receives child-related credits for claiming the child, they have to re-pay the IRS.   

It might be too late for this tax year, but you can get an IP PIN (it is a 6 digit number) to use for your child to prevent anyone from claiming your child.

If your Social Security number is compromised and you know or suspect you are a victim of tax-related identity theft, take these additional steps:

• Respond immediately to any IRS notice; call the number provided.
• Complete IRS Form 14039, Identity Theft Affidavit. Then print and mail or fax according to the instructions. 
• Continue to pay your taxes and file your tax return, even if you must do so by paper.

6-digit IP NUMBER FROM IRS

https://content.govdelivery.com/accounts/USIRS/bulletins/2af48f0?reqfrom=share

to get you new PIN from the IRS

- https://www.irs.gov/identity-theft-fraud-scams/retrieve-your-ip-pin

All of that being said......is there a signed agreement -- Form 8332 -- between you and the other parent?

Are you the custodial parent?  Do you have an agreement with the other parent to allow the other parent to claim them--due to divorce or that you live apart and share custody?  Did one of you sign a Form 8332?

If there is a signed 8332 then the custodial parent retains the right to file as Head of Household, get earned income credit and the childcare credit.  The non-custodial parent gets the child tax credit for children under the age of 17.

As far as the IRS is concerned, the custodial parent is the one with whom the child spent the most nights during the tax year--at least 183 nights.