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We study spin-dependent transport and spin polarization through two asymmetric quantum dots (QD’s) embedded in the arms of an Aharonov-Bohm (AB) ring, in which spin splitting produced by external magnetic fields is incorporated into a tight-binding model Hamiltonian. This device shows a sensitive spin-polarization effect by manipulating either in-plane or perpendicular magnetic fields. In particular, an extremely small Zeeman splitting leads to a reversal of the polarization polarity in the differential weighted spin-polarization function. Finally, we demonstrate that the degree of spin polarization is affected by the additional AB effects in the ring. In comparison, the polarization is substantially lower through a single QD in a one-dimensional system.