Bike broke, strange parts came out, and doesn't know where to find exact replacement
It is a derailleur pulley, and fairly worn out one at that. The easiest way to find a fitting replacement is to buy a set from an aftermarket manufacturer that comes with adapter shims for different derailleurs. You can simply try different shims until you find the one that fits.

They do come in different teeth counts. From the picture it looks like this one used to have 11 teeth.