You cannot get the American Opportunity Credit for working on a PhD. The AOC is only available to students pursuing an undergrad degree. However you may be able to get the Lifetime Learning Credit for graduate study. The LLC is not refundable---it can reduce your tax liability.
https://ttlc.intuit.com/questions/3262983-who-is-eligible-to-take-the-american-opportunity-tax-credi...
https://ttlc.intuit.com/questions/1901172-what-education-tax-credits-are-available
https://ttlc.intuit.com/questions/1901526-what-s-the-income-limit-for-the-american-opportunity-and-l...
https://ttlc.intuit.com/community/credits-and-deductions/help/what-expenses-qualify-for-the-lifetime...
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