You file your tax return and include the children as dependents. If you are due a tax refund on your return the IRS will pay the refund.
You will have to print and mail the return if the your ex already e-filed with the dependents on their return and the IRS accepted the tax return.
See this TurboTax support FAQ for how to print and mail a tax return when using the online editions - https://ttlc.intuit.com/turbotax-support/en-us/help-article/printers-printing/print-mail-return-turb...
Within a year the IRS will be mailing both you and the ex a letter to investigate who was entitled to claim the children as dependents on the tax return. The loser of the investigation will have to pay back any tax refund based on the dependents along with penalties and interest.
