Hi,
Sorry I was not around to answer this earlier. Hopeully you found the answer elsewhere, but for other people reading...
Peppers need to be completely ripe for best germination. So you need to wait until they are red as green ones are immature.
Remy

Thank you for answering! I brought the pepper plant inside and the peppers turned red without much sun. Collected lots of seed, there were just a few that's turned black. On the other hand, I have another pepper plant - Yolo Wonder and, it seems, I waited for too long as some seeds germinated inside the peppers.

Yes, seeds will sometimes sprout if you wait too long. Seeds normally have a mechanism in them to not sprout inside of the fruit. but if the temp and humidity are right, it can happen. Obviously conditions were right were for the Yolo Wonder :)