Yes, if you claim your oldest child and file your 2024 return, and then a final return is filed on behalf of your children's father for 2024, also claiming that child, then that second return will be rejected from e-filing, and removing the dependent may affect the refund or balance due on that return.
The amount of difference to the tax owed with his final return would depend on the amount of his total income and other factors. When a second return is e-filed claiming the same dependent, the return is automatically rejected from e-filing. The IRS may send both claiming parties an audit letter requesting documentation to establish which taxpayer is entitled to the dependent.
As @DawnC advised above, and as shown in the IRS references she cited, you are entitled to claim your child who lived with you as a dependent regardless of the wording in the divorce decree. You would normally prepare IRS Form 8332 and provide it to the other parent in order to waive your right to claim your dependent.
See this TurboTax article for more information on duplicated dependents. The second taxpayer to claim the same dependent could file by mail to avoid the return being rejected from e-filing, but the IRS would still normally contact both taxpayers in order to determine which is entitled to the dependent.
@Dweste
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