TurboTax is asking if "you" in generic terms, meaning anyone on your return, had a 1095-A. So you will enter it as if it is yours. The Marketplace policy number will identify the person covered as your mother. It is in a way "your" policy as far as the IRS is concerned when it comes to the Premium Tax Credit if you are claiming the person who is receiving the credit.
You should be aware, that if the Premium Tax Credit was calculated based on your mothers income, and you are claiming her with more income, it is possible that you would end up being responsible for paying the credit back offsetting any gains you may have by taking the Other Dependent Credit or by claiming Head of Household (if that would be your filing status simply because you are claiming your mom)
You can walk through the steps of entering the 1095-A and see how it affects your return. If it is a negative affect, you can then delete your mother from your return by clicking the trash can next to her name in the Personal Info section and then going to Tools>>Tax Tools>>Delete a Form>>Delete next to the 1095-A and 8962.
Obviously, if it has a positive affect on your return, you would not want to delete her or the 1095-A.
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