The quantum kicked particle in a magnetic field is studied in a weak-chaos regime under realistic conditions, i.e., for general values of the conserved coordinate x(c) of the cyclotron orbit center. The system exhibits spectral structures ["Hofstadter butterflies" (HBs)] and quantum diffusion depending sensitively on x(c). Most significant changes take place when x(c) approaches the value at which quantum antiresonance (exactly periodic recurrences) can occur: the HB essentially "doubles" and the quantum-diffusion coefficient D(x(c)) is strongly reduced. An explanation of these phenomena, including an approximate formula for D(x(c)) in a class of wave packets, is given on the basis of an effective Hamiltonian which is derived as a power expansion in a small parameter. The global quantum diffusion of a two-dimensional wave packet for all x(c) is briefly considered.