  We study a lattice fermion model for superconductivity in the presence of an
antiferromagnetic background, described as a fixed external staggered magnetic
field. We discuss the possibility that our model provides an effective
description of coexistence of antiferromagnetic correlations and
superconductivity, and its possible application to high temperature
superconductivity. We also argue that, under certain conditions, this model
describes a variant of the periodic Anderson model for heavy fermions. Using a
path integral formulation we construct mean field equations, which we study in
some detail. We evaluate the superconducting critical temperature and show that
it is strongly enhanced by antiferromagnetic order. We also evaluate the
superconducting gap, the superconducting density of states, and the tunneling
conductivity, and show that the most stable channel usually has a
$d_{x^2-y^2}$-wave gap.
