You cannot "write off" a gift.   Gifts to individuals are not deductible.  If you own the home and just let your mother live there, you can use the mortgage interest on your tax return and treat the home as a second home.   You will still be subject to the SALT limit of $10,000 for all of your combined state and local property taxes.  Is your name on the mortgage?

The mortgage interest that you pay for your mother's home can only be deducted as part of your return if the home is considered to be your second home. 

You can deduct mortgage interest for your main home and a second home as part of your Schedule A Itemized Deductions.  You do not have to use the second home as your home in order to claim it as your second home.

There is not another option available to claim the mortgage interest.  Gifts are not a deduction.

It cannot be your second home unless you were listed on the mortgage and/or deed in 2020.