Student Pilot reported a rough running engine after takeoff and returning in the pattern for an immediate landing.

Narrative

Was starting the flight portion of my private pilot check ride in Aircraft X. Me and the DPE did a thorough preflight inspection of the aircraft and went through the documents prior to flight; we both determined the plane was in an airworthy condition for flight. Started the plane and ran through all checklist with no problems; did the run up and everything looked normal on the ramp; left mag had about a 50 RPM drop and the right had a 50-75 RPM drop; carb heat normal drop as well. Plane was leaned for taxi and the taxi was normal; no indications of engine roughness. Went mixture full forward for a soft field takeoff and the engine was normal throughout takeoff; systems in the green at 2;000 RPM. At about 600 ft. went to cruise climb of 90 kts.; Tower told us to contact Departure; Departure gave us 'altitude our discretion'. After reading back the 'altitude our discretion' the engine went quiet for a moment; almost like it skipped a beat. Then within 3 to 5 seconds later it happened again; as soon as this happened Name the DPE told me to keep climbing and turn back towards the runway and we talked to Approach. They asked what the problem was and we notified that we were having possible engine issues. They told us to follow the aircraft in front of us and asked if we wanted any services on the ground. At this point; Approach told us they were calling [for priority handling] and that we were cleared to land on XXR. I performed a forward slip to a landing and landed without any issues. Once on the ground we continued to notice slight engine roughness. The fire trucks followed us from the runway back to the ramp just to make sure everything was alright. The DPE tried to run a quick diagnostic of what happened but didn't want to run the engine up too much that close to ramp parking. He did do a 'soft' mag check of the mags with the engine idled at 1;000 RPM. At this point we shut down the engine and parked the plane.