There are forms you can download to report this kind of thing. However, I have to say that the IRS mostly does not care. I know because I have been through the same thing. I assume you are paying alimony in which case you get the deduction.
Take a look at the following TurboTax article for some advice in your situation: What if somebody already claimed my dependent?
In general, if you are the parent that is eligible to claim the child, but he/she has already been claimed, then you should file your return by mail. This will prompt the IRS to examine both tax returns and request additional information to determine which return was filed correctly.
You could consider filing your return without claiming your dependent and then amending your return later to add the dependent back. This would also prompt the IRS to examine both tax returns.
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Someone else claimed my dependent and my return was rejected
If someone else claimed your dependent already, then your e-filed return will be rejected. Print, sign and mail your own return which claims your dependent. Mailed returns are processed differently by the IRS. It will take some time (maybe even up to a year) but eventually the IRS will contact both parties and sort out who could rightfully claim the dependent. The person who wrongfully claimed the dependent will face repayment of refund $, plus penalties.
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.