Problem with Fiesta's smart charging

[ENVIOclev]

Greetings to all, I own a 2010 Fiesta 1.4 petrol engine and I'm from Turkey. I've been dealing with charging issues for nearly three months now, ever since I purchased this vehicle. Battery life is satisfactory at 12.6-12-7 volts when the vehicle is not in use. While it's running, it stays at a maximum of 13.2. The alternator that I replaced did not work. Then I replaced it with a pre-owned, authentic one that I bought online; it fits perfectly! Ultimately, it was the previous one that was substituted.
Before leaving yesterday, I made sure the voltage was 12.7 volts, which it was when the car wasn't working, and it was. The shifting began to knock on the road at an unexpected moment. My recent discharge and recharge of my battery, along with smart charging, is likely to blame.
I need some assistance figuring it out.

[ENVIOclev]

Amazon.co.uk : alternator

[EnchantedScribe]

Battery and alternator diagnostics.. Evaluation of Power Source

Include the steps you took, the voltage you obtained, and the results you posted for each.

[NAVITEL]

After you've done the previous tests, you can see if the alternator produces a better or higher output without the limit input by removing the small wire connector plug from the alternator and then starting and running the engine again. Despite the fact that the battery indicator light will most likely illuminate, I anticipate that it will.

The shifting (I assume it's automatic) doesn't seem to have anything to do with this issue, and I don't get why you would suspect a problem when the battery was 12.7V the day before, after no use, and everything seemed to be working fine.