TT does catch it. Be sure you entered the 1099-G in the correct location in Federal taxes, Wages and Income, Unemployment.
Turbo Tax didn't catch unemployment as non taxable in NJ. When I was unchecking the box as not state income in NJ, it didn't let me file as e-file and now somehow I proceed without check mark it has been added as taxable income in NJ and total amount of tax in NJ has gone up by about $900.
How can I edit income again in NJ section to exclude unemployment income?
Unemployment has never been taxable in NJ, and TT does handle this correctly. Why do you think it isn't?
Because if I was checking the box as my unemployment income not as NJ state income then TT keep showing me error, but once I unchecked it it included in my income. Now TT charged my cc about $245 before this happened. Now I am unable to edit my NJ income because it's already imported my all info from federal. NJ tax went up about $900 because of unemployment income of about $11K.
I didn't file my tax yet and it needs to be corrected before I file.
Just enter the 1099-G in Federal > Wages and Income > Unemployment. Don't check any special boxes for iA.
(and I'm not sure what boxes there are to check anyway. Did you enter the 1099-G in the wrong place in Federal?)
It is not taxable if you live in NJ, but might be taxable if you live in another state and are receiving UE Comp from NJ.