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Based on your information - your mother is your household employee.Please be aware that wages paid to your parent are NOT subject to social security and Medicare taxes
See IRS publication 926 page 5https://www.irs.gov/pub/irs-pdf/p926.pdf
Wages not counted. Don't count wages you pay to any of the following individuals as social security or Medicare wages, even if these wages are $2,000 or more during the year.3. Your parent. Exception: Count these wages if both the following conditions apply.a. Your parent cares for your child who is either of the following.i. Under the age of 18, orii. Has a physical or mental condition that requires the personal care of an adult for at least 4 continuous weeks in the calendar quarter services were performed.b. Your marital status is one of the following.i. You are divorced and haven't remarried,ii. You are a widow or widower, oriii. You are living with a spouse whose physical or mental condition prevents him or her from caring for your child for at least 4 continuous weeks in the calendar quarter services were performed.
You are asking about child tax credit - but most likely - you meant - a credit for the child care expenses - that is a different credit.Here is a publication related to that credit
and yes - you are eligible to use the expenses paid to your mother if your mother is not your dependent.
On the other hand - payments you made to your mother is her taxable income - and while these payments are not subject to social security and Medicare taxes - these are still subject to income tax - and if you mother has other income - she might be required to file the tax return.