The Coulomb coupling、the Kazama-Yang coupling-кqβ∑·r/2Mr3 and the coupling iкzzde2γ·r/2Mr3 between a charged spin-1/2 fermion and a Dirac dyon are considered simultaneously. It is shown that for all the angular momentum states the fermion's radial wave functions have the physically reasonable asymptotic behavior at the origin. The bound state condition is qualitatively analysed. We show that, in the fixed dyon field when the extra magnetic moment к→0, the bound states of fermion exist, but in the fixed monopole field when к→0, the bound states of fermion do not exist.