Beechcraft pilot reported a NMAC while on a GPS approach. After ATC had given a traffic alert; the pilot's traffic system became active and a light twin engine jet passed 50 feet below. The pilot continued the approach while the Controller apologized for the mishap.

Narrative

I was PIC on an IFR flight into ZZZ. In the right seat my passenger is an IFR rated pilot who has several thousand hours. Approach on XXX.XX cleared me on the GPS XX approach at an altitude of 2000 to the IAF of ZZZZZ while on the segment from there to the IF of ZZZZZ1 at an airspeed of 120 kts. Approach called out traffic to my east which my Garmin G500 TXI; GTN 650 and screen showed at 1300 ft. below us. My passenger and I looked to the east could see nothing until within a few seconds the Garmin Traffic alarms when off and a light twin jet flew about 50 ft. under us; I could see the pilot in the front seat! No evasive action would have been possible in the time I had. As I continued the approach the Controller apologized for what happened and turned me over to ZZZ. Later that day I reviewed our flight on ADS-B found that at XA:19 at our altitude there was a jet traveling at 275 MPH on a heading of 265 degrees than one minute later 350 degrees leveling off at 2900 ft. and 252 MPH. The aircraft continued orbit in the ZZZ1 area.ZZZ1 does have a clearance delivery and the ZZZ Approach frequency for that airport is the same one that I was on. My fellow pilot and I never heard Approach talking to the jet. From ADS-B it appears that the jet took off from ZZZ1 on a heading of 226 then turned right almost perpendicular to our flight path. They came in a blind spot blocked by our wing. I have the latest Garmin Traffic System in my ADS B system in my Beechcraft. The ZZZ airport was very busy as evidenced by the Tower told me I was sixth to land when I checked in after the hand off from ZZZ Approach. If I had been at the altitude prescribed on the Runway XX approach plate I would have been at 2700 ft; it still would have been close but not fifty ft. On a telephone call with Approach Control after the incident they told me the minimum vectoring altitude on this segment was 1600 ft. ZZZ1 is located close to class B airspace. Something needs to be done to protect the airspace between ZZZ1 and ZZZ. With the large cargo jets and other fast traffic at ZZZ I am very concerned about the overlap in traffic between the two airports.