No, it is not correct (assuming the child is a full-time student under age 24 and the student is not filing as MFJ).

As for how to 'fix' it in PTO, you'll need to look around or wait until somebody that knows PTO comes by.

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@skyworks wrote:

did not claim the depend, let the student claim himself.

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No.  If the somebody is ELIGIBLE to claim the student, the student can NOT "claim himself".  He must indicate that he CAN be claimed.  There should be another option to say that although he CAN be claimed, nobody is actually claiming him (which will allow the student to claim the non-refundable part of the credit).   When you fix that, that MIGHT also 'fix' things with the American Opportunity Credit.