I did some research as well as asked multi lawyers on this subject.. so severance is not considered pay in NJ being it is for past work with company due to years of service. so you do not have to claim it . here what i came across.. check with your local laws before not claiming it.
Severance pay is not considered income
The state of New Jersey does not consider severance pay to be income when calculating whether or not a person should be able to receive unemployment. The only way that severance pay could affect unemployment benefits is if the employment relationship is extended in any way by the severance package. In other words, if you remain on the active payroll of a company, you will not be able to collect unemployment.