Where are NJ Anchor payments for seniors recorded on Federal Tax Returns?

First, determine which year and if it is a reduction or possibly taxable. NJ Division of Taxation - Answers to Frequently Asked Questions - NJ.gov states:

• If you receive a refund or rebate of real estate taxes this year for amounts you paid this year, you must reduce your real estate tax deduction by the amount refunded to you. 
• If the refund or rebate was for real estate taxes paid for a prior year, you may have to include some or all of the refund in your income.

Second, 

• if it was current year, simply reduce your real estate tax and you are done.
• if it was a prior year - determine did you take the standard deduction or itemize on the federal.
  • If you took the standard deduction, it isn't taxable and you are done.

Finally, since you itemized in a prior year, determine how much of it is taxable. See Pub 525 page 27 to determine if any portion is taxable. 

Did you receive a 1099-G and which box has the payment? Some states make it hard to enter a rebate. If you can't get the G entered in either of the 1099-G spots, follow these steps to enter the income:

1. go to the federal income section
2. scroll to the bottom
3. Miscellaneous Income, 1099-A, 1099-C, Start
4. Scroll to the bottom
5. Other reportable income, Start
6. Other taxable income?
7. Select YES
8. Description  -1099-G for NJ Property Rebate
9. Amount, enter your amount of
10. Continue