I inherited a mortgage. I hold it the other party pays me monthly. are these (income) payments to me reportable

Think of the mortgage as an asset with a value, which is the principal balance remaining, like a stock holdings.  That asset is not taxable to you when you inherit it, just a like a stock is not taxed when you inherit it.  However, if the stock pays dividends, that is taxable income to you.

In the same way, the interest portion of the mortgage payment is taxable income to you.  Your borrower should have an amortization schedule prepared by the original lender, or there might be a copy in the lenders's financial papers or loan documents.  That will show the amount of interest contained in each payment.  If you don't have an amortization schedule, you may want to prepare one for the borrower, that you both agree on.  If the mortgage is perfected (listed with the county as a lien on the property) then the borrower is allowed to take a tax deduction for the interest, and the figure they deduct should match what you report as income.  Also, I believe the borrower needs your social security number or tax ID number to report the interest so they can take the deduction.