Well before you try more drastic measures like a Factory Reset, don't stop at least trying to find out just which app or service is behind that occasional, weird 'clinking' sound. If anything, use Samsung's Smart Switch utility to make a full backup of your user account. It will make doing a restore of your data easier if necessary, and it's always a better practice to have backups of your phone anyway. Backups are important, they really are.
www.samsung.com
But getting back to that sound, since you don't see anything in the Notification log that correlates with when it does occur that is odd but it's not an absolute. You also mentioned not seeing anything notable as far as apps that 'might' be responsible but keep in mind that there could be several menus, conditionally-accessible menus, and annoying-messy-to-use sub-menus to look through now. Each version of Android includes an increasingly complex Settings menu, and add in that Samsung opts to extensively add/alter even more complexity, there's often multiple options to check for things like Notification sounds. Looking through the User Manuel for your model, there are several on pg. 102 through pg. 107 to go through as a starting place:
If nothing in those Settings options stop that sound, you might want to then try looking through the
Running services menu to see if there is some app or Android background service might be responsible for that sound. Note that
Running services won't indicate outright about that sound, it will show you a more extensive listing of all the processes that are active and loaded in RAM. Also, you need to enable the
Developers Options menu that's otherwise hidden within your Settings menu (it's an integral part of the Android OS, it's just something that needs to be intentionally made visible):
Android ships with a whole bunch of Developer Options that can unlock experimental and debugging features. Here's what these options do.
www.xda-developers.com
Anyway, once you enable
Developers Options, use
Running services and see if perhaps there's some system related service might be making that sound. Note that there's likely to be one or several
Android System items and if you tap on them that will reveal more info on just which service or services it refers to. So yeah, this involves a lot of speculation on your part. Just be very judicious about anything you change in
Developers Options. There will be a lot of oddly named system processes that appear to be gibberish to some but vital as far as keeping your phone functional.