  We study the tunneling density of states (DoS) in the superconducting systems
driven by Zeeman splitting E_Z into the paramagnetic phase. We show that, even
though the BCS gap disappears, superconducting fluctuations cause a strong DoS
singularity in the vicinity of energies -E^* for electrons polarized along the
magnetic field and E^* for the opposite polarization. The position of the
singularity E^*=(1/2) (E_Z + \sqrt{E_Z^2- \Delta^2}) (where \Delta is BCS gap
at E_Z=0) is universal. We found analytically the shape of the DoS for
different dimensionality of the system. For ultrasmall grains the singularity
has the form of the hard gap, while in higher dimensions it appears as a
significant though finite dip. Our results are consistent with recent
experiments in superconducting films.
