Does it happen when you play any particular note or is it whenever you play anything on that string (even open)? The action of that string may be too low for the guitar which would cause the string to touch the edge of the neck, the bridge, or the pickups and cause a plinking sound. You can try to raise the bridge up a little bit to see if that fixes the problem, but if you do this you will also have to reset the intonation of the guitar.