PA-28 student pilot reported engine roughness and partial power loss during cruise. Pilot diverted and landed safely.

Narrative

Planned solo cross country: ZZZ1-ZZZ2-ZZZ3-ZZZ1 (Did not make it back to ZZZ1; diverted to ZZZ)Requested priority handling on flight services; as well as the ZZZ CTAF; once switched over to ZZZ CTAF; engine roughness experienced; and a slight loss of engine power. I did a thorough preflight around XA:00 at ZZZ1 which after that I requested flight following to ZZZ2.I departed ZZZ1 RWY-XX safely at around XA:30 to the South-West. I landed safely at ZZZ2 around XB:06 and then departed to the East for ZZZ3. Picked up another flight following to ZZZ3; it was a safe and uneventful flight from ZZZ2 to ZZZ3; landing around XB:50 .After departing ZZZ3; I flew toward the East; and picked flight following to ZZZ1. Approximately 10-NM to the Southwest of ZZZ I started to experience engine roughness and immediately notified ZZZ Center and told them about the situation; and that I would monitor the engine instruments; and let them know if I would need to divert.As soon as I started losing power slightly I requested priority handling with ZZZ Center; and started flying toward ZZZ. I was advised to switch to the CTAF at ZZZ. I also requested priority on the ZZZ CTAF frequency; and landed on the closest available runway; Runway-XY at XC:50; and taxied safely to the FBO.I was asked by ZZZ center to contact Flight service and let them know about the situation; which I did and then also called my instructor to inform him that I had landed safely. One of the FBO staff confirmed that he heard Engine roughness when I was landing.