PA28 pilot reported returning safely to departure airport after experiencing a sputtering rough-running engine.

Narrative

I was flying Aircraft X. After completing the engine run-up at the hold-short area of Runway XXL at ZZZ; I contacted ZZZ Tower; advising them I was number one holding short of Runway XXL; awaiting IFR release.Upon receiving my release; I was directed to fly a heading of 280° and was cleared for takeoff on Runway XXL. Upon entering the runway; I advanced the throttle to full power and began the takeoff roll. Throughout the takeoff roll; the engine instruments were in the green and well within parameters to continue the takeoff.After rotation; upon reaching approximately 600 feet MSL; I was directed to contact ZZZ Approach. After establishing initial contact; I advised that I was at 1;000 feet MSL; climbing to 2;000 feet MSL per my clearance. ZZZ Approach then instructed me to climb and maintain 4;000 feet MSL and maintain my current heading.Approximately two minutes later; ZZZ Approach cleared me direct to the ZZZZZ fix. At this time; the aircraft was climbing through approximately 2;700 feet MSL. As I began the left turn to proceed to the fix; I experienced a rapid power loss from the engine. Prior to the power loss; the engine was running at approximately 2;400 RPM; and the aircraft was in a nose-up attitude; climbing at Vy (~79 KIAS).The power loss was immediate; dropping to 900 RPM; followed by extreme rough running. I rolled out of the turn; leveled the wings; and confirmed the engine was still producing very limited power. I immediately executed the Engine Power Loss In Flight checklist: I turned on the electric fuel pump; switched the active fuel tank; and applied carburetor heat. These actions did not resolve the issue; and severe power loss continued.At that time; I advised ZZZ Approach that I needed to cancel my IFR flight plan and return to ZZZ. The controller asked for the nature of the situation. I responded that I was experiencing severe power loss and requested priority handling. ZZZ Approach acknowledged the request; confirmed my IFR cancellation; and issued vectors to ZZZ. Shortly thereafter; the controller instructed me to contact ZZZ Tower.Upon contacting ZZZ Tower; I advised that I was a priority aircraft experiencing severe power loss and needed to return to the field immediately. The local controller instructed me to enter a left downwind for Runway XXL and asked for the nature of the situation. Initially; due to task saturation; I advised that I would begin a left downwind for Runway XXL and reiterated that I was experiencing rapid; severe power loss.After providing this information; the local controller advised me of the current wind conditions and offered the option to land on Runway XYR. Due to the situation and my experience landing with a tailwind; I advised that I would land on Runway XYR.During descent through approximately 1;800 feet MSL; the engine continued to run rough; sputtering intermittently. Based on prior experience with power loss; I remained well above the VGSI until I was assured I would make the field. Once certain of reaching the runway; I employed a slip maneuver to lose altitude.Approximately 1 NM from Runway XYR at about 1;100 feet MSL; I advised the Tower that I would be making a right 360° turn to ensure I would not overshoot the runway. The controller approved the maneuver as requested. After completing the 360°; I was on glidepath with the VGSI for Runway XYR.I landed the aircraft with no flaps; touching down just beyond the aiming point on Runway XYR. Due to the tailwind; I allowed the aircraft to roll out to Taxiway 1. Upon clearing the runway at 1; with the engine still running rough; I immediately shut down the engine.Approximately 30 seconds later; I was met by local fire rescue and airport operations. After confirming the aircraft was not at risk of fire or explosion; I exited and provided my information to responding personnel. Airport operations contacted my school; which dispatched a tug to Taxiway 1 and towed the aircraft back to the ramp with no further incident. The aircraft was delivered to the maintenance facility and is currently awaiting diagnosis.During my preflight inspection of the aircraft; no deficiencies were found or identified. I used a fuel sump on both wings ensuring there was no water or contaminants in the fuel tanks. I also inspected the oil and engine from the access hatch and confirmed it was well within the parameters defined by the manufacturer. The airframe; flight control; and onboard systems inspections also showed no deficiencies or abnormalities. During the engine runup procedure there were also no deficiencies. The magneto test for both magnetos yielded a drop of 100RPM on each magneto. The carburetor heat test yielded a 60RPM drop. And during the engine idle check the RPMS remained in the low 800s. The electric fuel pump test on and off validated positive fuel flow after switching tanks on the ground. It also validated positive fuel with the electric fuel pump on and off.It is worthy to note that this is not the first time I have experienced a severe engine power loss inflight with the airplanes operated and maintained by my school. The most recent being in another aircraft. Having cited in my previous report questioning the integrity of the maintenance department; today's incident has proved that there is something wrong with the way these airplanes are maintained. It is entirely unacceptable that these aircraft are being released onto the line especially considering the fact that they are used for training and instruction. The maintenance logs show there was a similar issue that took place in the same Aircraft X citing an engine roughness and spark plug issue also during the climb. The alleged cause for this was the belt separating from the AC compressor. This airplane received a 100hr inspection and had 41.3 remaining on the Tach. Again the condition of these aircraft is grossly unacceptable and action needs to be taken. If not pilots who fly these aircraft; especially students; are at a exponential risk for becoming victim to the poor maintenance and becoming involved in a tragic accident; one that may unfortunately result in casualty.