In this work, we have investigated some aspects of the new more general exponential cosine screened Coulomb potential (NMGECSCP) in noncommutative three-dimensional real space-phase (NC:3D-RSP) for one electron atoms through the generalized Bopp's shift method in the framework of four infinitesimal parameters <$ETHETA ( chi )> and <$Etheta bar ( sigma bar )> due to (space-phase) noncommutativity, by means of the solution of the deformed Schrodinger equation (DSE). The perturbation property of the spin-orbital Hamiltonian operator <$EH sub so-ges (r,~THETA ,~theta bar )> and new Zeeman Effect operator <$EH sub z-gec (r,~chi ,~sigma bar )> are investigated and the corresponding energy eigenvalues <$EE sub {ges-(d,~mu )}> (<$Ep,j~=~l~symbol С~1 "/" 2,l,s>) and <$E sub z-gec (p,~m)> are easily calculated. The new eigenvalues reduce to known results in quantum mechanics if <$E( THETA ,~theta bar )~symbol Ъ~(0,~0)>. We have shown also that, the global quantum group (GQG) of (NC:3D-RSP) reduce to new subgroup symmetry of NC three-dimensional real space (NC:3D-RS) under three-dimensional NMGECSCP interactions.

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