Abstract <p>High-frequency fluorescent radiation by incoherently pumped polar two-level quantum system possessing permanent electric dipole moments and simultaneously interacting with external low-frequency field and dissipative environment of some kind was studied. The system in question may be represented by a one-electron two-level asymmetric polar semiconductor quantum dot characterized by the electric dipole moment operator with unequal diagonal matrix elements in its ground and excited quantum states. An analytical expression for the steady-state fluorescence spectrum as a function of the amplitude, initial phase and carrier frequency of the driving field, as well as of the pumping intensity, was derived. It was shown that in the case of strong external field an interaction with the environment is modified, which modification alters in its turn the fluorescence spectrum.</p>