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A model for 3:2 high-frequency quasi-periodic oscillations (HFQPOs) with 3:2pairs observed in four black hole X-ray binaries (BHXBs) is proposed byinvoking the epicyclic resonances with the magnetic connection (MC) between aspinning black hole (BH) with a relativistic accretion disc. It turns out thatthe MC can be worked out due to Poynting-Robertson cosmic battery (PRCB), andthe 3:2 HFQPO pairs associated with the steep power-law states can be fitted inthis model. Furthermore, the severe damping problem in the epicyclic resonancemodel can be overcome by transferring energy from the BH to the inner disc viathe MC process for emitting X-rays with sufficient amplitude and coherence toproduce the HFQPOs. In addition, we discuss the important role of the magneticfield in state transition of BHXBs.

A model for 3:2 HFQPO pairs in black hole binaries based on cosmic battery