How many times has the light actually come on and of those times how many times did you actually get the codes read? I ask b/c if you’ve had the codes read multiple times and consistently come up with P0302 then I’d say to stay on the 2nd cylinder - specifically check the compression just to rule out mechanical fault before chasing your tail about other things.
But if you’ve only had the codes read once, but the light and rough running have occurred multiple times I’d actually worry more about the connection to refueling and rough running. One possibility is that you overfill your gas tank (continue past when it clicks off) and/or have a bad vent valve in the tank. After filling you may end up with liquid fuel in your evaporation lines which then causes the engine to run too rich after you start it up. In this case, maybe one time the code is P0302, another time P0301 or P0300 or even an evap system code.
Is the check engine light always associated with refueling?