The most important parameter driving the solar wind-magnetosphere interaction is the southward (Bz) component of the interplanetary magnetic field (IMF). While the dawn-dusk (By) component of the IMF is also known to play an important role, its effects are usually assumed to be independent of its sign. Here we demonstrate for the first time a seasonally varying, explicit IMF By-dependence of the ring current and Dst index. Using satellite observations and a global magnetohydrodynamic (MHD) model coupled with a ring current model, we show that for a fixed level of solar wind driving the flux of energetic magnetospheric protons and the growth-rate of the ring current are greater for By<0 (By>0) than for By>0 (By<0) in Northern Hemisphere summer (winter). While the physical mechanism of this explicit By-effect is not yet fully understood, our results suggest that IMF By modulates magnetospheric convection and plasma transport in the inner magnetosphere.