Penalty weeks are assessed, in addition to the overpayment, when you make a false statement or misrepresentation. The number of penalty weeks is determined by several factors, including the amount of overpayment. Penalty weeks must be served by claiming otherwise eligible weeks. It is similar to having extra "waiting weeks" on a claim. Penalty weeks remain in the system for five years after the decision is issued. Serving penalty weeks does not lower the overpayment.
If you are ineligible for regular unemployment benefits because you must serve penalty weeks, you are likely eligible for the Pandemic Unemployment Assistance (PUA) program. You should apply for PUA and file a weekly PUA claim for each week of your penalty weeks. The minimum weekly PUA benefit is $205, and if you get PUA you will also get the extra $600/week (ends July 25). The weeks you get PUA benefits do not count towards removing your penalty weeks.