The authors deal with the quantization of the dynamical systems for which the Hamiltonian vector fields of observables form a deformation of \(n\)-dimensional oscillator algebra. After giving some results of the geometric quantization theory, they organize the considered mechanical systems as Kähler symplectic manifolds of constant holomorphic sectional curvature. Then, they apply the geometric quantization approach. Finally, it is considered an extension of the quantization to Kähler manifolds, not necessarily of constant holomorphic sectional curvature, admitting \(H\)-projective holomorphic mappings.