We apply the extended (statistically consistent, SCA) Gutzwiller-type approach to the periodic Anderson model (PAM) in an applied magnetic field and in the strong-correlation limit. The finite- U corrections are included systematically by transforming the PAM into the form with the Kondo-type interaction and the residual hybridization, both appearing at the same time and on equal footing. This effective Hamiltonian represents the essence of our Anderson–Kondo lattice model. We show that in ferromagnetic phases the low-energy single-particle states are strongly affected by the presence of the applied magnetic field. We also find that for large values of hybridization strength the system enters the so-called locked heavy fermion state introduced earlier. In this state the chemical potential lies in the majority-spin hybridization gap and, as a consequence, the system evolution is insensitive to further increase of the applied field. However, for a sufficiently strong magnetic field, the system transforms from the locked state to the fully spin-polarized phase. This is accompanied by a metamagnetic transition, as well as by a drastic reduction of the effective mass of the quasiparticles. In particular, we observe no effective mass enhancement in the fully polarized state. The findings are in overall agreement with experimental results for the Ce compounds in high magnetic fields. The mass enhancement for the spin-minority electrons may also diminish with the increasing field, unlike for the quasiparticle states in a single narrow band in the same limit of strong correlations.