We consider a Potts-$XY$ model in two dimensions as a generalization of the Ising-$XY$ model which described the Josephson-junction array under a magnetic field. We show that the transition is of first order and thus exclude for the present model the presence of a huge screening effect as it was emphasized in the Ising-$XY$ case. We give some arguments that this conclusion holds for the latter case.[ postscript.gz]