There is no federal "care giver credit". The situation your describe does not qualify for any credit or deduction.
If your mother qualified as you dependent, you could claim her as such and get her $4050 exemption (deduction). You would also be able to deduct any medical expenses you paid for her*.
Dependent rules: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
*If your close relative cannot be your
dependent because he/she had more than $4,050 of gross income, but otherwise would
have qualified as your dependent (basically that you
& other family members provided more than half his support), then you can
include in your deductible medical expenses any qualifying medical expenses you
paid on his/her behalf just as if he/she was your dependent.
