In this study, for the first time, the combined effects of external magnetic, electric, and Aharonov-Bohm (AB) flux fields on quantum levels of the hydrogen atom embedded in Debye and quantum plasmas modeled by the more general exponential cosine screened Coulomb (MGECSC) potential are investigated within cylindrical coordinate formalism using the asymptotic iteration method. The MGECSC potential includes four different potential forms when considering different sets of the parameters in the potential. The corresponding Schrodinger equation is solved numerically in order to examine both strong and weak regimes and confinement effects of external fields. The influence of screening parameters of the MGECSC potential on quantum levels of the hydrogen atom is also studied in detail in the presence of external magnetic, electric, and AB flux fields. As it is possible to model both Debye and quantum plasmas by using screening parameters in the MGECSC potential, the effects of each plasma environment on quantum levels of the hydrogen atom are also considered in the external fields. It is observed that there are important results of external fields on the total interaction potential profile, and the most dominant one in these fields is the magnetic field. Furthermore, the effects of confinement on the physical state of the plasma environment is a subject of this study. These details would be important in experimental and theoretical investigations in plasma and atomic physics fields. Published by AIP Publishing.