It's a screw. You undo it to remove the bolt, I think.
The round bit is the actual screw, the clip sort of thing is there to keep the screw from working itself loose, I think, as all of that is part of the bolt so it goes flying backwards fairly violently (especially as the Bergmann No. 1 is a simple blowback). So you'd need some sort of retaining clip. IF that looks weird, well, remember it's from 130 years ago.
The knurling on the screw face is to help you hold on when you rack the bolt.
Reference the Forgotten Weapons video on the real pistol, at roughly 9:30 :
Because the pistols are very old and very rare, Ian doesn't actually disassemble it, and and while the part is shown on the patent drawings 15 minutes or so of search has failed to turn up the actual patent, where the parts are explained. (I didn't look very hard, mind you, so if you really want to know I'd suggest a more detailed hunt for the 1892 Austrian patent.) So there's a certain amount of guessing.
The 1896 Bergmann No. 2 still has the screw but the clip thing is gone, so I'm guessing it didn't really do whatever it was intended to do.