You have a basis in your IRA as far as NJ is concerned because you did not deduct IRA contributions from your NJ taxable income in all those past years.
Those are unrecovered.
See Worksheet C in the NJ Resident Return Instructions for how to avoid double taxation on that money (i.e. recover it) when you withdraw from your IRA.
For an Inherited IRA, the NJ basis is the basis of the original owner from whom you are the beneficiary.
You probably don't have this information so you pay tax on the entire distribution.
Inherited IRAs must be treated separately form your own IRAs.
If the original owner was not an NJ resident there is no NJ unrecovered contribution.
