An analytical theory is developed for studying the phenomenon of generation of third harmonic radiation by the propagation of circularly polarized laser beam in homogenous underdense quantum magnetoplasma by using recently developed Quantum hydrodynamic (QHD) model. The effects of quantum Bohm potential, quantum statistical Fermi pressure and electron spin -1/2 have been taken into account. A circularly polarized laser beam propagating through quantum plasma produces density oscillations at second harmonic. The density oscillation combined with the oscillatory velocity produces third order current density, which derives third order harmonic radiation. The field amplitude of third harmonic radiation with reference to the fundamental amplitude of the incident circularly polarized radiation and the conversion efficiency for wave number-mismatch has been analyzed. It is observed that the efficiency of generated third harmonic is affected significantly due to the magnetic field strength, plasma electron density, intensity of circularly polarized laser pulse and quantum diffraction effects.