N90 TRACON Controller reported an NMAC with an IFR and a VFR aircraft.

Narrative

Aircraft X was on the JAIKE Arrival and checked in at 7;000. I descended him to 4;000. As he was leaving 5;000; I saw VFR traffic at 4;000 westbound and told him to stop his descent and maintain 4;500 and to climb back up if he needed to and advised him of the traffic. The VFR was on a 1200 code but ADS-B showed a call sign of Aircraft Y. Another aircraft checked in and while I was talking to him; [a] conflict alert went off the VFR [that] was just east of Aircraft X at this point. I reissued the traffic; only now realizing the VFR had also climbed to 4;500 but I couldn't see the altitude because it was covered by the data blocks of Aircraft X and Aircraft Z; another VFR on frequency. I realized they were co-altitude as I was calling traffic but it was already too late to do anything. The targets merged at 4;500 and Aircraft X did not acknowledge the call. After the conflict was over I asked Aircraft X if he got an RA as I was shocked they didn't climb or descend. He said yes and I asked if it was climb or descend to which he replied we were just trying not to hit; he was coming right at us and turned left at the last minute. When I shipped Aircraft Z to PHL Approach he made a remark that those two planes were very close."We have daily TCAS RAs and [it's] not uncommon to have NMAC reported in the EWR sector. This is the worst I have seen but it is a frequent occurrence with satellite arrivals in the vicinity of SBJ VOR and also further north around MMU and TEB. With the volume of satellite traffic and the complexity of the airspace around EWR; TEB; and CDW; the airspace needs to be redesigned. There need to be at least some Class C or B corridors to run all these IFR arrivals through and keep them away from VFR aircraft that are not in communication. In this case I tried to apply vertical separation; which failed; but it is not uncommon to try to vector around a VFR only to have the make a 180-degree turn back into your traffic. Without being in communication with the VFRs there is no way to really ensure separation and see and avoid is just not always feasible or safe either. Also; there should be some dedicated practice areas made so that we don't end up with the VFR Aircraft A's constantly doing air work and turning into IFR traffic. Additionally; we need to increase the staffing in the area. We were fortunate that this occurred during the part of the day when we had staffing to keep Metro open but it has become the new norm to have Metro combined with Yardley when it really needs to be open all day; every day on a normal shift."