PA-32 student pilot reported a loss of control and departure from the runway pavement resulting in damage to the landing gear.

Narrative

I departed ZZZ on a solo flight to practice pattern work and maneuvers from ZZZ. Winds were 180 at 7 kts. and skies clear. I departed the airspace and conducted steep turns at 3500 ft. MSL. After approximately 30 minutes I returned to ZZZ. Conditions on return were unchanged. I was instructed to join the full right downwind for XXR and midfield I was cleared by Tower for option number 1 and told to fly left traffic on the go. Abeam the runway I configured to land and on final I noticed that the wind had blown me slightly to the left of centerline. I corrected but wasn't happy with the approach and elected to go around at approximately 800 ft. AGL. As I went around I informed ATC. On the downwind I was instructed to extend for traffic; and Tower called my base and cleared me for option number 2.I confirmed with ATC that I had the C172 traffic in sight and turned to land. On final I was happy with both my speed and glideslope and continued to land. I rotated in ground effect and pulled power landing slightly flat but smooth. As I touched down the aircraft pulled to the right; into the wind; I then corrected to the left; which in hindsight may have been an over correction but this cannot be confirmed. The aircraft pulled left; I applied the right rudder and the aircraft began to skid right. At some point I began applying brakes but the aircraft exited to the right of the runway between 1500-2000 ft. Aircraft came to a stop approximately 50 ft. off the runway and initial damage appears to be limited to the right main strut; but this is currently under review by maintenance.