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A $(p,~q)$-deformation of the Landau problem in a spherically symmetric harmonic potential is considered. The quantum spectrum as well as space noncommutativity are established, whether for the full Landau problem or its quantum Hall projections. The well-known noncommutative geometry in each Landau level is recovered in the appropriate limit $p,~q = 1$. However, a novel noncommutative algebra for space coordinates is obtained in the $(p,~q)$-deformed case, which could also be of interest to collective phenomena in condensed-matter systems