Under the three-year rule, the pension payments that you receive are assumed to be a return of your contributions until you have gotten back the full amount that you contributed. Since you already paid New Jersey tax on the amounts that you contributed, they are not taxable on your New Jersey tax return when you get them back as pension payments. "Cost Recovered in Prior Years" is the cumulative sum of the amount you received in prior years that was not taxable because you were recovering your contributions.
If this is the first year that you are receiving this pension, the cost recovered in prior years is zero. After the third year (i.e. starting in the fourth year), the cost recovered in prior years will be equal to the annuity cost (your total contributions), and the full amount of your pension payments will be taxable. That's the meaning of the three-year rule. You recover (get back) all your contributions within the first three years.
If you use TurboTax every year, and always transfer information from the previous year's tax return when you start your new tax return, TurboTax will keep track of the cumulative amount recovered, and the cost recovered in prior years will be filled in for you.
