Since the credit is non-refundable, you will not receive a refund as a result of claiming the credit on your 2024 return. Receiving a refund is the only way it could be applied toward any past taxes that you owe and are paying currently. The IRS may take the refund to pay off the prior debt, but if you are already in a payment plan that may not be automatic.
The unused credit can be carried forward to help offset any future taxes for up to five years.
Your only possible option to offset the taxes you already owe would be if you were eligible to claim the adoption credit in 2023, but did not, and the taxes that you owe were for that same year. Then it could be beneficial to look at amending the 2023 return to claim the credit in 2023.
See the following TurboTax help article to learn more:
How do I claim the Adoption Credit in 2024?
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