Narrative:

I was working a satellite sector and had an IFR release off of ZZZ airport for [aircraft X]. [Aircraft X] was filed for a west bound SID climbing into the flight levels. When [aircraft X] departed I got an automated point out with departure control which was combined at arrival sector. The automated point out was approved. I climbed [aircraft X] to 16000 ft. And sent the aircraft on course. A few seconds later; arrival sector called me on the landline to combine departure control and arrival to me. During the brief I was told about a VFR PA31 (aircraft Y) conducting a photo mission at 11500 ft. I was briefed that they were working southwest to the northeast. I failed to see that [aircraft X] and [aircraft Y] were on converging courses. [Aircraft X] was climbing; at what I thought; was an expeditious pace. The arrival controller called me on the landline while doing his sector briefing overlap and asked if I was watching [aircraft X] and [aircraft Y]; which I was not. At that point; the mode C of [aircraft X] was 11000 ft. And the two aircraft were right at 3 miles apart. I told [aircraft X] to expedite their climb for traffic; and at that point; [aircraft X] stated that they were descending for a TCAS RA. [Aircraft X] said that they have the aircraft in sight and are descending. I did not issue a traffic call or traffic alert since [aircraft X] stated they had the aircraft in sight. I issued traffic to the photo mission aircraft; [aircraft Y] twice; but [aircraft X] responded both times thinking I was talking to them.my supervisor stated that the two aircraft got 2.1 miles and 500 ft. Apart. I yelled out that I had an aircraft respond to a TCAS RA; but the supervisor did not hear me; and I did not make sure that the management knew. The pilot then climbed back to 16000 ft. And I transferred communications to center. When the aircraft was in their destination TRACON's airspace; I was told that the pilot told the approach controller that he almost had a near midair. The pilot called our TRACON and did not mention a near midair; and my supervisor explained that I made a mistake and missed the traffic.better situational awareness on my end. I was not sure how far the photo mission flew before they turned around; so I need to clarify that during the briefing.

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Original NASA ASRS Text

Title: TRACON Controller reported NMAC with two aircraft within their sector.

Narrative: I was working a satellite sector and had an IFR release off of ZZZ airport for [Aircraft X]. [Aircraft X] was filed for a west bound SID climbing into the flight levels. When [Aircraft X] departed I got an automated point out with Departure Control which was combined at Arrival Sector. The automated point out was approved. I climbed [Aircraft X] to 16000 ft. and sent the aircraft on course. A few seconds later; Arrival sector called me on the landline to combine Departure Control and Arrival to me. During the brief I was told about a VFR PA31 (Aircraft Y) conducting a photo mission at 11500 ft. I was briefed that they were working southwest to the northeast. I failed to see that [Aircraft X] and [Aircraft Y] were on converging courses. [Aircraft X] was climbing; at what I thought; was an expeditious pace. The Arrival controller called me on the landline while doing his sector briefing overlap and asked if I was watching [Aircraft X] and [Aircraft Y]; which I was not. At that point; the Mode C of [Aircraft X] was 11000 ft. and the two aircraft were right at 3 miles apart. I told [Aircraft X] to expedite their climb for traffic; and at that point; [Aircraft X] stated that they were descending for a TCAS RA. [Aircraft X] said that they have the aircraft in sight and are descending. I did not issue a traffic call or traffic alert since [Aircraft X] stated they had the aircraft in sight. I issued traffic to the photo mission aircraft; [Aircraft Y] twice; but [Aircraft X] responded both times thinking I was talking to them.My supervisor stated that the two aircraft got 2.1 miles and 500 ft. apart. I yelled out that I had an aircraft respond to a TCAS RA; but the Supervisor did not hear me; and I did not make sure that the management knew. The pilot then climbed back to 16000 ft. and I transferred communications to Center. When the aircraft was in their destination TRACON's airspace; I was told that the pilot told the approach controller that he almost had a near midair. The pilot called our TRACON and did not mention a near midair; and my supervisor explained that I made a mistake and missed the traffic.Better situational awareness on my end. I was not sure how far the photo mission flew before they turned around; so I need to clarify that during the briefing.

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.