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ABSTRACT We perform magnetohydrodynamic simulations of accreting, equal-mass binary black holes in full general relativity focusing on the effect of spin and minidiscs on the accretion rate and Poynting luminosity variability. We report on the structure of the minidiscs and periodicities in the mass of the minidiscs, mass accretion rates, and Poynting luminosity. The accretion rate exhibits a quasi-periodic behaviour related to the orbital frequency of the binary in all systems that we study, but the amplitude of this modulation is dependent on the existence of persistent minidiscs. In particular, systems that are found to produce persistent minidiscs have a much weaker modulation of the mass accretion rate, indicating that minidiscs can increase the inflow time of matter on to the black holes, and dampen out the quasi-periodic behaviour. This finding has potential consequences for binaries at greater separations where minidiscs can be much larger and may dampen out the periodicities significantly.