N.J. Stat. Ann. § 2A:44-131

The lien given by and filed pursuant to this article shall have priority over an assignment, by a contractor or subcontractor to a third person of moneys due or to grow due to such contractor or subcontractor for labor performed or materials furnished for a public improvement referred to in this article even though such assignment was made prior to filing of notice by the lien claimant, but not if such money had been paid to the assignee at the time of the filing of notice.