  The effective interaction of the electron magnetic moment anomaly with the
Coulomb field of superheavy nuclei is investigated by taking into account its
dynamical screening at small distances. The shift of the electronic levels,
caused by this interaction, is considered for H-like atoms and for compact
nuclear quasi-molecules, non-perturbatively both in $Z\alpha$ and (partially)
in $\alpha/\pi$. It is shown that the levels shift reveals a non-monotonic
behavior in the region $Z\alpha>1$ and near the threshold of the lower
continuum decreases both with the increasing the charge and with enlarging the
size of the system of Coulomb sources. The last result is generalized to the
total self-energy contribution to the levels shift and so to the possible
behavior of radiative QED effects with virtual photon exchange near the lower
continuum in the supercritical region.
