When you live together unmarried, only one parent claims the child and all tax benefits. The other parent should not list the child at all, to prevent confusion.
First you need to decide which parent will claim the child. It is usually better for the parent with the higher income to claim the child, unless the parent with the lower income qualifies for EIC. You may need to test both situations. (You can make extra online accounts to test each scenario with disposable user names and passwords.)
Then, if you have decided your partner will claim the child but you filed first, this is what will happen.
1. Your partner claims the child on their return. In the custody questions, answer "NO" to the question about a shared custody agreement about who will claim the child. (This only applies to legal agreements between divorced or separated parents living apart.) If your partner answered "yes" to the agreement question, it is possible they did not get all the tax benefits of the child. You may want to delete the child and re-enter them, being careful about all the questions.
Then your partner will have to print their return, sign it, and mail it to the IRS with copies of their W-2 and any other required forms and pages, using the printed instructions. You can't e-file a state if you mail your federal so you will also have to sign and mail their state return. The e-file block on your dependent's SSN will not be lifted this season, even if you amend right away. Your partner is stuck mailing their returns.
2. You will need to amend your return to completely remove the child. Wait until your original refund is paid, just in case the IRS makes some adjustment that would have to be accounted for. Then you can prepare, print, sign and mail your amended return. You may have to include a payment to repay any dependent credits you received in error.
