State tax filing

I have been trying to ask HR and payroll to add NY wages information with 0 dollar withheld into W2c.  They just keep spinning.  My question is,

 

Should W2 list the all states which have tax withholdings (my case NJ), or, should it list all the states which are subject to tax withholding (my case NY and NJ, NY withholding zero)?

 

 If it is the first case, I will have to go with the current one because I do not think they will correct the entire year’s accounting.  If it is the second case, I will keep trying to have a W2c.