In this study, interaction between core-shells nanoparticles and quantum dots is discussed via the full-quantum-theory method. The electromagnetic field of the nanoparticles is derived by the quasistatic approximation method and the results for different regions of the nanoparticles are quantized from the time-harmonic to the wave equation. Utilizing the optical field quantization, the nanoparticles' and quantum dots' deriving amplitudes contributing to the excitation waves are determined. In the current model, two counterpropagating waves with two different frequencies are applied. We derived the Maxwell-Bloch equations from the Heisenberg-Langevin equations; thus the nanoparticles-quantum dots interaction is perused. Moreover, by full quantum analyzing of the analytical expression, the quantum-plasmonic coupling relation and the Purcell factor are achieved. We show that the spontaneous emission of quantum dots can be dramatically manipulated by engineering the plasmon-plasmon interaction in the core-shells nanoparticles. This issue is a very attractive point for designing a wide variety of quantum-plasmonic sensors. Through the investigation of the nanoparticle plasmonic interaction effects on absorbed power, the results show that the nanoparticles' and quantum dots' absorption saturation state can be switched to each other just by manipulation of their deriving amplitudes. In fact, we manage the interference between the two waves' deriving amplitudes just by the plasmonic interactions effect.