In this study, we have scrutinized the influences of the temperature \(\left(T\right)\) and hydrostatic pressure \(\left(P\right)\) on the nonlinear and linear optical properties of a core/shell quantum dot (QD) system with Screened Modified Kratzer potential (SMKP). To realize this goal, we have examined the energy levels and their associated wave functions using the diagonalization method within the effective mass approximation. Analytical terms for absorption coefficients (ACs) and relative refractive index changes (RRICs) are exploited by means of the density matrix approach. The numerical outcomes are offered for typical InAs/GaAs core/shell QD system. The dependency of SMKP, dipole transition matrix element and electron energies of the ground (\(1s\)) and first excited state (\(1p\)) on the \(P\) and \(T\) that are varied over a range. Obtained numerical calculation results revealed that the \(P\) and \(T\) impacts the magnitude and position of the resonant peaks that characterize the ACs and RRICs.