Small Aircraft; High Wing; 1 Eng; Retractable Gear
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 5
Other / Unknown
ATC Issue All Types; Conflict NMAC
Air Traffic Control Provided Assistance; Flight Crew Took Evasive Action
Aircraft
I was working Local Control and departed Aircraft X VFR right downwind to the east.  Initially; I issued traffic to the pilot that was approximately 3 miles northeast of his position. As the traffic converged; I gave Aircraft X a suggested right turn of 20 degrees to avoid traffic. I reached out to the traffic opposite direction and they happened to be inbound to the field with traffic in sight.  I gave Aircraft X an update of the traffic and they reported traffic in sight as well.  Aircraft X was instructed to resume own navigation and remain outside B with a frequency change.  No traffic was observed east of Aircraft X within the scope of my RACD settings.  Minutes later; Aircraft X reported a near miss with an aircraft that was westbound.  This occurred at least 10 miles east of MYF.  The traffic was outside of the scope of my RACD settings and I was unaware and unable to advise Aircraft X of that traffic.  By the time the Aircraft Y checked in; traffic was not a factor. Aircraft Y never had Aircraft X in sight. Pilot of Aircraft X was told to give the Tower a call on the land line.  I don't have any particular recommendations for the event. Our priority is to focus on the runways and aircraft in our airspace.  We provide additional services; however; there is a limit to how far we zoom out on our radar screens.  Being too focused on what's beyond the scope of our radar maps will take our eyes off of our D airspace and our runways and will result in a greater safety issue.
MYF Tower Local Control reports of a near mid air that was reported by a pilot after it left the MYF Class D.