Fuse box & circuit breaker for same apartment?

Hello, I live in an apartment building with a circuit breaker switch for each apartment in the basement and in my apartment is also a fuse box with 2 fuses. The circuit breaker is for both circuits. So my question is, if the breaker is set for 15 amps, does it matter if the fuse box has 20 amp fuses in it? I know that's not ideal, but I'm just wondering. It seems that the breaker would already capping usage at 15 amps, but I know nothing about electricity. The situation is, one fuse blew after about 20 years, and the hardware store was all out of 15s so I bought a 20. I'll get 15 amp again when I can, but just wondering about safety for now. Thank you!