I fitted a new tap to a sink, single cold water tap. When I first turned it on the water ran fine. If I open the tap further, the water flow becomes jerky with constant gaps in the flow.
Is this the tap that is malfunctioning or the delivery?
I presume you turned the water off to install the faucet. This usually means that air is introduced into the piping, and can cause spurting as it bleeds out. Leave the water running for a few minutes and see if it stops.
Also, ensure that you've turned any shut-offs all the way back on.