No, you don't need to enter the 1095-A on your child's tax return since you are claiming them as your dependent. Your child won't have any health insurance questions to answer on their return. TurboTax will tell them "Since someone is claiming you on their 2024 taxes, you don't have to complete Health Insurance".
You can review this TurboTax article I'm on my parents' 1095-A form. What do I do on my return? for more information.
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