Yes. Box 9b on the 1099-R shows the amount of the employee "contribution" to the retirement plan and is important in lowering how much of your distribution is taxable.
"Basis" in a retirement plan is also called "cost" or "contribution". In a word, it is the amount of after-tax dollars that the taxpayer contributed to the retirement plan over the years while he/she was employed.
When the taxpayer retires, then the pension or annuity from the retirement plan begins. As the payments are made to you, each payment consists of a little bit of that "basis" and a lot of the money that the company is contributing.
You don't owe tax on the "basis" that is paid to you each period, because the "basis" is after-tax dollars that you contributed - and you don't get taxed twice on the same money.
The employer's contribution is, of course, taxable. This means, for example, that if a taxpayer received $12,000 in pension payments, that perhaps only $11,600 might be taxable if $400 of the payments were the return of the "basis".
There is a Simplified Method that determines the amount of "basis" that is included in each periodic payment, so that the return of the "basis" to the taxpayer is spread out over an actuarial life span.
You have two loaded questions here. Please read through the entire post as the questions are also related.
First, NJ state exclusion:
What is Box 9B on your 1099-R and how to handle it:
If the taxpayer didn't make any after-tax contributions to the retirement plan (as is often the case), then the "basis" is zero, and each distribution from the retirement plan is 100% taxable.
Since you have an amount in box 9b, this means that you have basis in the retirement plan, and you want to enter that instead of zero.
When you enter the 1099-R, make sure to enter box 9b. And when you see the entry for "plan cost" in the Simplified Method interview, make sure that you put in the amount in box 9b, if it's not already there.
The result should be that the taxable amount of the pension should be somewhat less that the gross distribution, because part of the gross distribution was the return of a small amount of what was in box 9b.