If I refinancing my California residence so I can purchase an apartment for my son in NYC for cash is the rent my son will pay (to pay off my loan) taxable?

If your son pays you rent then you're considered a landlord and must report the rent you receive as taxable income.  To offset your rental income, the IRS lets you deduct expenses and depreciation related to the rental. The link below has information on how to report your rental income and expenses.

https://ttlc.intuit.com/replies/3288530

Is it an issue that one of the rental expenses is for a loan on a different prperty?