We suggest, for the first time, the more general exponential cosine screened Coulomb (MGECSC) potential to investigate the positronium (Ps) atom immersed in Debye and quantum plasmas. Ps atom immersed in Debye and quantum plasmas under spherical confinement is examined by solving the corresponding Schrodinger equation via the tridiagonal matrix method. The MGECSC potential has four different sets to model Debye and quantum plasmas. But, we consider only two sets as the screened Coulomb (SC) potential for Debye plasma and the MGECSC potential for quantum plasma. The results of the confinement and the plasma screening effects on the energies, radial matrix elements, dipole polarizabilities and oscillator strengths of Ps atom are obtained, discussing in detail. It is worthwhile to specify that the spectroscopic features of Ps atom located in only plasma environment enable detailed information about plasma environment. The MGECSC potential is proposed to model various interactions of Ps atom immersed in plasma environment. In this study, the necessity and details of the MGECSC potential is discussed.