Your inherited IRA does not count as a retirement saving contribution. Nor does your contribution to your HSA.
Only your personal contribution to a 401(k), 403(b), SIMPLE IRA, IRA account counts for the saver's credit.
Please read this TurboTax article for more information.
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Unlike non-spouse beneficiaries, if you are the surviving spouse of the decedent, the distribution from the inherited IRA reduces the amount of your new retirement contributions that are used to calculate the retirement savings contributions credit.