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

Estimating the radiative part of QED effects in systems with supercritical charge