Jax TRACON controller reported an aircraft had a near midair collision with another unidentified VFR...

Narrative:

Aircraft X was southbound at 3;000 feet. There was a VFR aircraft northbound at 3;000 feet. I called traffic and issued a right turn to avoid. A moment later; I was on the landline. While on the line; aircraft X calls that he is taking evasive action due to a VFR aircraft. I did not issue a traffic alert since the pilot was already maneuvering. I initially thought that the VFR traffic was the previously called traffic. Upon later review; I saw that it was actually a different aircraft. The VFR was southwest of aircraft X; southbound at 4;700 feet. The VFR aircraft made a fast; right descending turn towards aircraft X. I never saw the VFR aircraft make the turn; and I don't remember [a] conflict alert going off prior to me be being on the landline. I have no specific recommendations. However; if the adjacent TRACON stars had a feed with our stars system; inbound information could be handled via automation rather than landline coordination. This may have given me enough time to see the event develop.

Original NASA ASRS Text

Title: JAX TRACON Controller reported an aircraft had a NMAC with another unidentified VFR target that the Controller confused for other VFR traffic.

Narrative: Aircraft X was southbound at 3;000 feet. There was a VFR aircraft northbound at 3;000 feet. I called traffic and issued a right turn to avoid. A moment later; I was on the landline. While on the line; Aircraft X calls that he is taking evasive action due to a VFR aircraft. I did not issue a traffic alert since the pilot was already maneuvering. I initially thought that the VFR traffic was the previously called traffic. Upon later review; I saw that it was actually a different aircraft. The VFR was southwest of Aircraft X; southbound at 4;700 feet. The VFR aircraft made a fast; right descending turn towards Aircraft X. I never saw the VFR aircraft make the turn; and I don't remember [a] conflict alert going off prior to me be being on the landline. I have no specific recommendations. However; if the adjacent TRACON STARS had a feed with our STARS system; inbound information could be handled via automation rather than landline coordination. This may have given me enough time to see the event develop.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1710127
Time
Date	201912
Local Time Of Day	0001-0600
Place
Locale Reference	JAX.Airport
State Reference	FL
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	Small Transport
Operating Under FAR Part	Part 91
Flight Phase	Cruise
Route In Use	Vectors
Flight Plan	IFR
Aircraft 2
Make Model Name	Any Unknown or Unlisted Aircraft Manufacturer
Flight Phase	Cruise
Route In Use	None
Flight Plan	VFR
Person 1
Function	Approach
Qualification	Air Traffic Control Fully Certified
Events
Anomaly	ATC Issue All Types Conflict NMAC

Jax TRACON controller reported an aircraft had a near midair collision with another unidentified VFR target that the controller confused for other VFR traffic.