When mower in gear, clutch pedal jumps; can this be fix?

Sounds like you may have a Vari-Drive rider. Probably a Sears or another brand made by AYP.

You should have a plate in front of the driver where the parking brake engagement lever is located.

You can remove the plate by removing the two hex head screws and inspect the belts and Vari-Drive double pulley.

If the belts appear worn or damaged, they need to be replaced. That would be a very difficult job and should be left to a good mower mechanic.

If the belts don't seem damaged or worn, you can at least add some spray lubricant to the center of the double pulley and to any idler pulleys you see.

Good luck!