Why cant there be hole current in the conduction band?

In a semiconductor, the conduction band is filled with electrons, which are negatively charged. Holes represent the absence of electrons in the valence band, not in the conduction band. Since the conduction band is typically occupied by electrons, it cannot have holes; instead, holes exist in the valence band where electrons are missing. Therefore, while there can be free electrons in the conduction band, holes are specifically a feature of the valence band.