Welcome to JustAnswer.
Since you already looked online and saw that New Jersey does not have an option for requesting the payment history you know that you must call.
The only option would have been to print your confirmation for each week when you certified. The confirmation screen provides the gross and net amount of your payment, the amount deducted for any refunds or garnishments, tax withheld on your payment, and tax withheld year to date. It will also give the remaining balance on your claim. When you go into your certification you can look to see if there is an option to print past confirmations. I cannot see anything past the general because I do not have a case with NJ unemployment.
If you cannot find something on the past confirmations, then the only other option NJ offers is to call and request the information.
Customer: I've been trying to call to claim my benefits for this week. I keep getting a message that the call volume is high and to call back. I've been trying since Tuesday and can't get anyone on the phone.
Robin D: You can go online to certify - http://lwd.dol.state.nj.us/labor/ui/ui_index.html
Have you ever done that?
The above link explains how to certify and what you will need.
Customer: I have been claiming my benefits on the internet for the past several months, but I now get a message that I cannot claim online but instead to call. I've been trying to call and can't get anyone to answer.
Robin D: I wish you had other options, but if their system requires you to call then that is what you will have to continue to try to do. There is no special place that will allow you to get around that. It is unfortunate that you have not been able to get through yet.