Low voltage

I have an 02 Hyundai accent 1.6 the car would not do over 25mph check engine light came on trouble code said low voltage I bought a new battery and when I tightened the alternator belt it ran great for four months then did it again so I tightened up the belt again and it ran great again for a week it said again low voltage and would not go over 25mph so I put a new alternator belt and it ran great but when I check voltage with multimeter it reads 14.05 volts idling when I turned the AC on it drops down to 12.49 volts idling but it slowly drops voltage down to 12.1 volts do I need to replace the alternator? The car is an 02 and only has 50k on it......

 

When giving description of diagnostic trouble codes, it is preferred to put in the proper format
PXXXX. That would help us understand what you're talking about.

If done properly then the alternator would not need to be tightened so often.
So, either the tightening was done wrong (which I doubt)
Or, there is a developing problem with the alternator.
If you do decide to change the alternator then be sure to clean all terminals and cables
This includes battery posts and cable terminals
One really can't see all corrosion. So best is to do some cleaning