OP; It looks hinkey and I don't know what it is. Could it be a front stem mount cable stop from an old pair of canti's or center-pull brakes (if so, it is one from the wrong stem diameter and thus it could mash off to the side). Example might be a 28mm or a 25.4mm stop on a 0.833 stem or something like that. Also could be a mount for an old headlamp, handlebar bag, etc. The missing picture from the other side should have clues.

First lesson in bike mechanics should be... don't over tighten stuff. That just makes situation worse. Second lesson might be to "get a torque wrench" so you can take it apart, inspect, clean, grease and reassemble to spec. That will quite often get rid of squeaks and also often help you find little problems before they become expensive problems. Recommend the smaller wrench from Park Tools. Get a metric allen/hex-head bit set also...you will need them from about 4mm up to 12mm (check your bikes to see the range needed). A small set of metric sockets to fit your wrench also a good idea (it will be either 3/8" or 1/4"). Consult Sheldon's and the OEM pages for advice on how much torque to apply to this or that bolt depending on the thread and what alloy it is made out of. You can always post here also for advice on such as most of us who have the proper tools have used them here and there [;-**

Note: And yes about 40% of folks posting here, who otherwise routinely offer excellent advice, will then tell you that you don't need to waste money on a torque wrench. I am in the other 60% group and routinely get bikes in for expensive and avoidable repairs from that 40% group. I love taking their money!

Hope that helps
/K