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We propose the superintegrable generalization of Smorodinsky-Winternitzsystem on the $N$-dimensional complex Euclidian space which is specified by thepresence of constant magnetic field. We find out that in addition to $2N$Liouville integrals the system has additional functionally independentconstants of motion, and compute their symmetry algebra. We perform theKustaanheimo-Stiefel transformation of $\mathbb{C}^2$- Smorodinsky-Winternitzsystem to the (three-dimensional) generalized MICZ-Kepler problem and find thesymmetry algebra of the latter one. We observe that constant magnetic fieldappearing in the initial system has no qualitative impact on the resultingsystem.

$\mathbb{C}^N$-Smorodinsky-Winternitz system in a constant magnetic field