Under quasi-radial interplanetary magnetic fields (IMF), foreshock turbulence can have an impact on the magnetosheath and cusps depending on the location of the quasi-parallel shock. We perform three-dimensional simulations of Earth's dayside magnetosphere using the hybrid code HYPERS, and compare northward and southward quasi-radial IMF configurations. We study the magnetic field configuration, fluctuations in the magnetosheath and the plasma in the regions around the northern cusp. Under northward IMF with Earthward Bx, there is a time-varying plasma depletion layer immediately outside the northern cusp. In the southward IMF case, the impact of foreshock turbulence and high-speed jets, together with magnetopause reconnection, can lead to strong density enhancements in the cusp.