We investigate the radiation properties of a driven exciton-biexciton structure quantum dot placed close to a graphene sheet. The study of the Purcell factor then demonstrates the tunability of light-matter coupling, which in turn provides the possibility to control the steady-state populations. As the result, dipole transitions can be selectively enhanced and asymmetry in the resonance fluorescence can be observed. Meanwhile, both quadratures can exhibit two-mode squeezing at the Rabi sideband frequencies. A further study shows that although the increase in the environment temperature has a d...