We have an old house built in 1924. The faucet in our bathroom sink needs replaced but I can't find one that will work.

It is a three piece faucet that looks similar to a wall mounted faucet but it is attached to the sink. It is NOT mounted on the top of the sink. The sink is mounted to the wall and there is a 3-4" ledge that we can set things on. The faucet is mounted to the front of that.

Could someone help? I don't want to replace the sink - just the faucet.