A TRACON Controller reported an unidentified VFR aircraft flew into Class B airspace into confliction with an air carrier being vectored for a visual approach resulting in a NMAC.

Narrative

I was working the V sector. I gave Aircraft X a vector for a visual approach for Runway 4R. Later; H sector asked me to widen out the airliner for a westbound smaller aircraft departure. I did; I turned Aircraft X left heading 275 for his descent as well; and he was high. I told Aircraft Y to expect a turn onto the 4R localizer. I then saw VFR traffic within JRF airspace at 020 southbound. I saw the code change briefly to something besides XXXX. I asked the W Controller if there was an IFR departure at JRF and that Controller was unaware of the traffic I was asking about. I called traffic to Aircraft Y; turned him and advised to level off if needed. Aircraft X reported the traffic in sight; I instructed him to maintain visual separation and continued to get him into the approach. I then asked him what type of aircraft it was because the aircraft had violated the Class B airspace. Aircraft X said it was a twin engine. The radar team monitored the VFR aircraft returning to JRF and got the aircraft information from the Tower there. Aircraft X called in and said it was a near mid-air.