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In this report, we show that the terahertz photoconductivity in Hg1-xCdxTe-based structures including a topological phase possess strong sensitivity to the external magnetic field polarity. We demonstrate that the photoresponse is an uneven function of the magnetic field applied. This behavior is atypical for the conductivity and photoconductivity which normally do not depend on the magnetic field polarity. Possible reasons for such an unusual effect are discussed.