Air carrier First Officer reported ground conflict with another aircraft with 10 feet of clearance during taxi into gate.

Narrative

We were taxiing to our gate XXX in ZZZ. There is a catering truck blocking the line. He's waiting for plane at [gate] XXY to park. Now we are blocking the north taxi line on the ramp and set the parking brake while we wait for truck to move. An RJ comes towards us at a normal taxi speed with his taxi lights on. He's on the north taxi line and doesn't appear to be slowing. I say on the radio; 'Ramp; Aircraft X; this RJ in front of us needs to stop. He's going to hit us.' Silence. Then I say; 'Aircraft Y needs to stop. My Captain is flashing our landing lights in his face. Ramp Controller says; 'Hang on; I'm talking to other ramp.' Without slowing he veers slightly away from us off of the taxi line and stops with about 10 ft. from his winglet to our nose. Ramp Controller says; 'He says he says he can make it.' I say; 'He is about 10 ft. from our nose; if he continues he will hit our wing. One of us needs to be towed.' He must have decided if he moves more into our empty gate spot that he could squeeze between our plane and the plane parked on the spot next to ours (XXX). Then he proceeds make a hard right turn to try; meanwhile; we wait to see if we get hit. He was able to clear both our aircraft and the aircraft parked at XXX. I asked the Ramp Controller for his call sign and she said Aircraft Y. Then we taxied into our gate without incident. Other aircraft pilots appeared to not be aware of how close they were to colliding with us until ramp controller asked them to stop. Other aircraft pilot should have stopped when we flashed our lights at them.