Ny Unemployment Weekly Certification Can I Claim NY Unemployment Insurance While Working As A Temp In NJ?

Can I claim NY unemployment insurance while working as a temp in NJ? - ny unemployment weekly certification

I live in New Jersey but worked in New York. I received unemployment insurance from New York Department of Labor files online.
I recently received a "full time" job with a temping agency (New Jersey) for an indefinite period. After the certification of the weekly issues ", I answered yes - I had a full-time job and not - the amount is more than weekly earnings 400.00 per week.

Questions:
I thought I was a week would receive compensation, minus what was collected. Am I wrong?
Will I be able to the balance of my winnings from NY right when I released from the repurchase or I shall sue in New Jersey?