In this study, for the first time, the combined effects of the external electric field, magnetic field, and confinement frequency on energies of two-electron parabolic quantum dots in Debye and quantum plasmas modeled by more general exponential cosine screened Coulomb (MGECSC) potential are investigated by numerically solving the Schrodinger equation using the asymptotic iteration method. The MGECSC potential includes four different potential forms when considering different sets of the parameters in potential. Since the plasma is an important experimental argument for quantum dots, the influence of plasmas modeled by the MGECSC potential on quantum dots is probed. The confinement frequency of quantum dots and the external fields created significant quantum restrictions on quantum dot. In this study, as well as discussion of the functionalities of the quantum restrictions for experimental applications, the parameters are also compared with each other in terms of influence and behaviour. In this manner, the motivation points of this study are summarized as follows: Which parameter can be alternative to which parameter, in terms of experimental applications? Which parameters exhibit similar behaviour? What is the role of plasmas on the corresponding behaviours? In the light of these research studies, it can be said that obtained results and performed discussions would be important in experimental and theoretical research related to plasma physics and/or quantum dots. Published by AIP Publishing.