The results of experimental research into characteristics of secondary penetrating radiation occurring when interacting primary X-ray beams from a solid-state cathode medium with targets made of various materials are reported. The experiments were carried out in a high-current glow discharge device with H2, D2 Kr, Xe gases and cathode samples made of Al, Sc, Ti, Ni, Nb, Zr, Mo, Pd, Ta, W, and Pt. The targets are shields made of various materials foil (Al, Ti, Ni, Zr, Yb, Ta, and W) with thickness of 10 - 30 μm and of 1- 3 mm. They were mounted at a distance of 21 and 70 cm from the cathode. In these experiments recording of the time radiation spectrums was carried out just before and after discharge current pulses (no discharge current). It was shown that the secondary radiation consisted of fast electrons. The secondary radiation of two types was observed. (1) The emission with a continuous temporal spectrum in the form of separate bursts with intensity up to 106 fast electrons a burst. (2) The emission with a discrete temporal spectrum and emission rate up to 109 fast electrons a burst. A third type of the penetrating radiation was observed as well. This type was recorded directly by the photomultiplier placed behind of the target without the scintillator. The abnormal high penetrating ability of this radiation type requires additional research to explain. The obtained results show that creating optically active medium with long-living metastable levels with the energy of 1.0-3.0 keV and more is possible in the solid state.