A321 flight crew reported ground conflict with another aircraft during taxi into gate.

Narrative

This particular day was day one and my first time flying into ZZZ. After landing; we were given instructions to taxi to gate xx via taxiway. B737 was instructed to taxi behind us to Gate YY after exiting the runway at the intersection. My taxi speed was anywhere between 10-15 kts. Being night time in an unfamiliar airport and the ramp having a restricted area; I was in no rush to taxi to the gate. Upon turning into the ramp to be lined up on XX; I slightly overshot the lineup due to unfamiliarity and not wanting to cross into the restricted area. When I turned further left to align myself with the taxi-in line; I saw the 737 racing past us at what seemed to be more than double our speed. My instructor and I were surprised at the reckless behavior of the jet. I promptly hit my brakes and turned to the right to avoid getting too close to the jet. The instructor keyed the mic and told the crew they cut us off. The response of the crew was something to the effect that we should turn off our taxi light to avoid blinding the ramp crew. It was apparent that the Captain did not agree with our assessment. This incident seemed to be an unnecessary and dangerous risk to everyone onboard both planes as well as the ramp crew.