That is usually a check valve in the city water connection failing, it could be it has gunk in it.
Turn off water pump, open faucet to de-pressurize, go outside to city water connection, carefully remove the screen/rubber washer and you will see a small plastic like pin in there, standing to the side (so you don’t get soaked from water), push it in and release it a few times, that is the check valve for when operating on water pump and not letting water back into the city water system if you happen to have hose connected up.
Put screen/rubber washer back on and turn on water pump to see if it stops coming out.
