I tried few things. LockCenter doesn't works, and even if you'll make it work like looping. It just locks mouse, the camera wont lock and rotate like in first person or shift lock. Soo what do I do? I read everything about this problem and the only solution was LockCenter, that doesn't works as intended...
The way you would probably want to go about doing this is forcing the player's camera into shift lock mode. Unfortunately I am not sure how to do this specifically but I found a dev forum post of somebody wanting to do this that got solved https://devforum.roblox.com/t/how-can-i-force-shift-lock/239206
If you don't want the player to be able to zoom in and out or limit it then all you need to do is select StarterPlayer and change some of the camera properties and play around with maximum and minimum zoom distance.
Hope this helps!