Welcome to TFL!
The pics are of a magazine for a semi automatic pistol, apparently in a small caliber. Tough to guess which without something for reference measurements.
There are a great many small auto pistols with magazines of that size and shape, possibly hundreds, since 1900. Dozens of European gunmakers made these "pocket" pistols, some in huge numbers, some in small quantities.
Common calibers are .25ACP (6,35mm Browning), .32 ACP (7,35mm Browning), and .380ACP (9mm Kurz/9mm Corto...). There are a couple other more rare calibers as well, but they are seldom seen.
Best thing I can suggest is to take the magazine to a gun show, and find the guy selling pistol magazines (there's almost always one or more at any show). See if he can match it to something he has. He might be able to, or he might not. But its your best bet.
Sometimes a magazine for an uncommon pistol will look nearly identical to one for a common pistol, with only a very small difference. You have to look very closely....
All else being equal (and it almost never is) bigger bullets tend to work better.