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We introduce a Hartmann system in the generalized Taub-NUT space with Abelianmonopole interaction. This quantum system includes well known Kaluza-Kleinmonopole and MIC-Zwanziger monopole as special cases. It is shown that thecorresponding Schrodinger equation of the Hamiltonian is separable in bothspherical and parabolic coordinates. We obtain the integrals of motion of thissuperintegrable model and construct the quadratic algebra and Casimir operator.This algebra can be realized in terms of a deformed oscillator algebra and hasfinite dimensional unitary representations (unirreps) which provide energyspectra of the system. This result coincides with the physical spectra obtainedfrom the separation of variables.

Quadratic algebra for superintegrable monopole system in a Taub-NUT space