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The Bronnikov generalization of the Fisher naked singularity and Dilatonic black hole spacetimes attracts high interest, as it combines two fundamental transitions of the solutions of Einstein equations. These are the black hole/wormhole "black bounce" transition of geometry, and the phantom/canonical transition of the scalar field, called trapped ghost scalar, combined with an electromagnetic field described by a non-linear electrodynamics. In the present paper, we put restrictions on the parameters of the Fisher (wormhole) and Dilatonic (black hole or wormhole) regularized spacetimes by using frequencies of the epicyclic orbital motion in the geodesic model for explanation of the high-frequency oscillations observed in microquasars or active galactic nuclei, where stellar mass or supermassive black holes are usually assumed.