No if you claim your mom as a dependent on your tax return.
Otherwise, yes and you have to provide your mom's name and SSN to claim child care expenses. She will have to report the amount you paid her as self-employed income.
The IRS says:
Payments to Relatives or Dependents - The care provider can't be your spouse, the parent of your qualifying individual if your qualifying individual is your child and under age 13, your child who is under the age of 19, or a dependent whom you or your spouse may claim on your return.
Please read this IRS document for more information.
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