I have cut edges of the screen on my TV. This problem doesn't appear in all games, but if it appears it is a little annoying. I looked into PS4 settings and I found the screen adjusting area option, and I set it as small as it was possible, but it not solved my problem. I was searching for some in-games options to adjust the screen size, but I didn't found any (now I am playing Fallout 76). Does exist some other way to calibrate screen size, excluding TV options? TV settings are correct, PS3 works fine, and I have never a problem with screen size there.
This is a TV problem that happens with most 720p or 768p, but rarely on 1080p or 4K displays.
As mentioned on the comments, this happens because of over scan. Some TVs have settings to modify or turn off the over scan, but other ones (specially cheap models) do not.
Now, to answer some things:
I found the screen adjusting area option, and I set it as small as it was possible, but it not solved my problem
That is because is up to the game developers to support it. Some games like the Hatsune Miku Project Diva series support it if set before the game is opened, others like GTA V allow it to change it while the game is running, and other games like Apex Legends just ignore it.