Interesting. But the answer is no, you cannot, unless the property is in your name. Your mother can claim it if you pay her directly and she uses the money you pay as "rent" as the property tax payment. She must claim the income from the rent and then the deduction on the taxes she pays. You cannot because in effect you are paying to live there which is rent.
If you pay the property tax directly to the state, you should stop doing that and pay rent which she can set aside to pay the taxes. Otherwise neither of you can claim the deduction.
If your mother has not other income other than your small rent and say her social security, then the amount you are paying is small enough so that she will neither have to lose her ss benefits nor pay income tax on your payments.
Social Security is set up so that people can have some income, it varies so I cannot quote for you, before they are required to pay taxes on it or reduce their benefits. She can call Social Security direct and get more information from them.