  A modified Hayward metric of magnetically charged black hole space-time based
on rational nonlinear electrodynamics with the Lagrangian ${\cal L} = -{\cal
F}/(1+2\beta{\cal F})$ is considered. We introduce the fundamental length,
characterizing quantum gravity effects. If the fundamental length vanishes the
general relativity coupling to rational nonlinear electrodynamics is recovered.
We obtain corrections to the Reissner--Nordstr\"{o}m solution as the radius
approaches infinity. The metric possesses a de Sitter core without
singularities as $r\rightarrow 0$. The Hawking temperature and the heat
capacity are calculated. It was shown that phase transitions occur and black
holes are thermodynamically stable at some event horizon radii. We demonstrate
that curvature invariants are bounded and the limiting curvature conjecture
takes place.
