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.
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