BE35 pilot reported degraded alternator performance along with rough running engine resulted in priority handling to a safe landing.

Narrative

- Aircraft had experienced degraded alternator performance over the previous two days.- I deemed that the aircraft was safe to fly as the alternator was providing sufficient; but not ideal; electrical output to the aircraft.- The flight plan was to fly from ZZZ1 to ZZZ2 via the ZZZ Bravo and ZZZ3 Bravo areas at 14;500 ft. Then; continue towards the ZZZ4 Bravo and terminate at ZZZ2.- In flight; all digital avionics and instruments were operational. All backup instruments were operational as well.- As I approached the ZZZ Bravo; I began feeling what I would describe as a persistent engine shudder or increased engine vibration which was new and unexpected.- The two reasons I determined this flight was no longer safe: it was unclear if this was related to the degraded alternator performance; and I would be flying into a 33kt headwind towards an area with a limited number of airports; and an even more limited number of services and assistance. Terminating the flight in ZZZ would be the best outcome.- I [requested priority handling] with ZZZ Approach and asked to land at ZZZ5. I received expedited assistance in entering the ZZZ Bravo.- I entered the traffic pattern at ZZZ5; landed; and rolled out without incident.I believe that the correct course of action was taken at every step of this flight given the information available at any given time. It is unclear if the two issues are related; but because one was already being actively monitored; I did not want to take any chances that it could be related in a way that wasn't clear to me.I met with a maintenance shop at ZZZ5 with whom I reproduced both the degraded alternator performance and engine shudder / vibration. The maintenance shop is currently continuing investigation based on my series of events and their findings on the ground.