Can I collect UI in NY if my F/T hours are cut to P/T hours, I refuse the offer and I quit?

I have tried to preserve my full time job by complying to requests made my boss in a recent employment evaluation over a specific time period. I submitted a progress report of all I did to preserve my employment on time. In response, I am told there will be a restructuring of my position, and my hours will be cut (at this time I don’t know to what degree). I would like to quit when a p/t offer is made and collect UI. Do I have the right to collect based on this circumstance?

Depends on how much they cut your hours. Generally, cutting someone’s hours are to save money, but from what you’ve said it sounds more like a punitive measure for a performance issue ..

In the meantime .. you should try to find a
precedent that might help you make a decision when you do know how much they will minimize your job .. because it may be a substantial change in the conditions under which you were hired.