I made $6k after tax contribution to traditional ira. Then I converted that to roth ira.I have $50k already in traditional ira so how much out of $6k is taxable by NJ?

TurboTax will figure out how much is taxable in NJ after you entered how much was previously taxed by NJ. Your traditional IRA contributions are not deductible in NJ. Therefore, if you only made contributions while living in NJ then all of your contributions will have been previously taxed.

Please go through the NJ state interview until you get the "Roth Conversion screen" and enter the amount of contributions that were previously taxed in NJ (click on the Learn More link if you need help figuring out the amount).

"In most cases, your contributions to a traditional IRA were already taxed by New Jersey and are not taxable when withdrawn. However, any amounts you roll over from a traditional IRA to a Roth IRA that were not previously taxed by New Jersey must be included as income on your New Jersey return the year they are withdrawn from the traditional IRA." (NJ Division of Taxation)

Thanks, So How Do I figure how much was taxed by NJ in prior years? My current $6k contribution is after tax so Can I put $6k as taxed by NJ? My traditional IRA has 50k balance out of which 45k is rollover from old 401k. Rest 5k  is contribution + earning. 

Yes, it would be $6,000 plus the amount of the previous traditional IRA contribution left in the account (all traditional IRA contributions are not deductible in NJ).

Thanks

Also to confirm rollover from old 401k to traditional IRA is not taxable event in NJ right? In other words, rollover 401k is not considered as a contribution to traditional IRA?

Yes, a rollover from 401(k) to a traditional IRA is not taxable in NJ. A rollover is not a traditional IRA contribution.