  The coexistence of antiferromagnetism with superconductivity is studied
theoretically within the t-J model with the Zeeman term included. The strong
electron correlations are accounted for by means of the extended Gutzwiller
projection method within a statistically-consistent approach proposed recently.
The phase diagram on the band filling - magnetic field plane is shown, and
subsequently the system properties are analyzed for the fixed band filling
n=0.97. In this regime, the results reflect principal qualitative features
observed recently in selected heavy fermion systems. Namely, (i) with the
increasing magnetic field the system evolves from coexisting
antiferromagnetic-superconducting phase, through antiferromagnetic phase,
towards polarized paramagnetic state, and (ii) the onset of superconducting
order suppresses partly the staggered moment. The superconducting gap has both
the spin-singlet and the staggered-triplet components, a direct consequence of
a coexistence of the superconducting state with antiferromagnetism.
