We study the electronic structure of a nonsymmorphic Kondo lattice system, CeCuX2 (X = As/Sb), a promising class of correlated topological materials important for advanced technology. While both the materials show Kondo behavior in their transport properties, CeCuSb2 is antiferromagnetic and no magnetic order is observed in CeCuAs2. We studied high-quality single-crystalline samples employing hard x-ray photoemission spectroscopy. The sample cleaving exposes the square-net structured pnictogen layers. The CeCuSb2 valence band indicates a highly metallic phase. The spectral intensity at the Fermi level in CeCuAs2 is weak, revealing close to semi-metallic behavior of the system. The Ce 3d spectra exhibit multiple features; the intensity of the features changes with the change in surface sensitivity of the technique, suggesting significant differences in the surface and bulk electronic structure. The bulk spectra of the Kondo system do not exhibit the typical f0-feature often observed in such materials. Instead, a distinct feature is observed at the lower binding energy side of the well-screened peak; the signature of this feature is manifested in the spectra from high-quality single-crystalline samples. This is outstanding and calls for physics beyond existing theories of correlated systems.