In this paper, the high-order quantum correlation effect is investigated in an asymmetric semiconductor quantum well with a three-level cascade-configuration structure, in which three dipole-allowed transitions are simultaneously driven by three laser fields. We find that the intensity-intensity correlation and intensity-amplitude correlation are strongly dependent on the relative phase and the Rabi frequencies of the driving fields. We assume that all of the Rabi frequencies for the three driven fields are identical. When the relative phase is 0, the intensity-intensity correlation shows strong correlation; otherwise, the normal correlations are obtained. On the other hand, the intensity-amplitude correlations are also modified by the relative phase. When the collective phase is taken as π/2 or 3π/2, the correlation functions in positive time region and negative time region is approximately symmetrical with each other. In addition, we also find that theintensity-intensity and intensity-amplitude correlations are strongly modified by the Rabi frequencies. When the collective phase is zero, the intensity-intensity correlation can be changed from strong correlation into normal correlation by modifying theRabi frequency; not only that, the values of third-order correlation can also be greatly enhanced during this process. In order to analyze the internal physics behind the above-mentioned phenomena, we use dressed-state transformation to calculate the decay rates in dressed-state picture. It is explored that there exits two closed decay channels between these dressed states, which lead to the occurrence of multiple quantum interference effects being responsible for the generation of the nonclassical higher-order correlation effects. Also, the dressed-state population is obtained at steady state. The result demonstrates that the quantum interference effects give rise to the coherent population trapping. When the atoms are trapped into the excited state, the anticorrelation is generated. In the other situation, the emitted resonance fluorescence photons show strong correlation when the atoms stay at the ground states. Importantly, the higher-order correlation effect in the semiconductor quantum well may be useful for the high-precision measurement and the detection of single-photon. It also may pave a way to explore the quantum properties of resonance fluorescence.