Fighting rings are characterised as being of a heavy duty than normal rings, and have ridges, spikes or protrusions on them. 

The Japanese have them, these have several names, and certain types of rings also individual names. Collectively called Katute, attributed to being in use by ninja. Used for fighting, poisoning, stabbing, restraining or climbing. Mainly they're made in iron, flat and with various spikes. One has an eyelet that a cord can be attached to.

The Bavarians had the signet ring shape, two are known to have spikes, others just heavy duty with a thicker protruding metal top.

The French Apache are know to have versions with grotesque faces, reminiscent of gargoyles, devils etc. Often with protruding features, eyes, noses, tongues, horns or ears. Mainly in aluminium. The Apache were known to be colourful and flamboyant probably the reason for the faces.

There are a few African examples but less is known about these. The ones I have seen are flat and made of iron, with one or a couple spikes.

Most are designed for applying pressure to nerve points, penetrating, ripping and tearing skin. Gives the user an advantage in a fight, is not a weapon that can easily be knocked out your hand, or taken from you, used on you, or will run out of bullets.

The rings have no palm brace like knuckles, and no government could pass a law banning rings, so they cannot ever be illegal. But this is also the reason most have disappeared, unless you know what they were, they'd just be tossed to one side, melted down for their metal or rust away with them being odd, ugly or uncomfortable. The forerunner to the classic bikers rings, but those are now mainly just fashion, with no or just proportional protrusions.