Yes, if you are paying interest on a loan legally set up like a normal mortgage by your family, meaning your family can take the home if payments are not made, or you have a legal binding instrument in addition to the loan you have as a mortgage, then you can deduct the interest on the loan. The family would be required to report interest income received and paid by you.
The legal documents must indicate that you are the owner of the property even though it is a mortgage held by your family. The payments themselves are not a deduction, only the interest. The rental property would be an asset using depreciation for the cost of the property (not loan payments themselves).
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