Small Aircraft; Low Wing; 1 Eng; Retractable Gear
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 4
Distraction
Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Air Traffic Control Separated Traffic
Human Factors; Environment - Non Weather Related; Procedure
Aircraft Y landing VPS was descending over V198 to FL200. Aircraft X; a departure from CQF in P31; was vectored NE bound to climbing to FL190 to allow Aircraft Y to descend south of the aircraft. Traffic was called to both aircraft. Aircraft X read back '200 Aircraft X' which was not caught or verified by the controller.The controller was busy separating aircraft arriving and descending to the northeast CEW landing VPS. When the controller noticed Aircraft X starting to climb; Aircraft Y was turned 25R to the southeast to try to get some lateral separation. At first since the targets were close; I thought it was MODE C interlace. Since I was unsure what altitude Aircraft X was climbing to I decided to try to get lateral separation instead of vertical. Upon further query Aircraft X misunderstood the traffic call and thought it was a climb to FL200.Traffic at the CEW sector has increased by multitudes over the past year due to numerous airlines starting and expanding service to the FL panhandle. Before COVID; the departure list from the 3 panhandle complexes (P31; Eglin RAPCON; and Tyndall RAPCON) rarely went over 30 proposed departures. Now we are regularly seeing 40-50 proposed departures.When the military airspace gets activated; the sector becomes an inverse T with about 10 MI on either side of the 'T' to separate commercial jets; slow props; military trainers; and fighters.The departures and arrivals are all filed over the same fix CEW creating a dangerous situation with minimal time to solve conflicts. There should be a redesign of this sector.
ZJX Center Controller reported an aircraft started a climb due to incorrect readback/hearback which resulted in a loss of standard separation.