Spin　polarization　through　a　four-quantum-dot　system　is　theoretically　studied　by　considering　the　effects　of　Zeeman　magnetic　field,　extrinsic　Rashba　spin-orbit　interaction　and　external　magnetic　field.　We　analyze　how　the　resonance　and　anti-resonance　bands　are　formed　by　means　of　the　mathematical　formula.　By　adjusting　the　external　magnetic　field,　the　spin　polarization　can　be　converted　between　-100%　and　100%,　which　suggests　a　physical　scheme　of　an　effective　magnetically-controlled　spin　filter.　The　combined　effect　of　external　magnetic　field　and　extrinsic　Rashba　spin-orbit　interaction　leads　to　spin-polarized　oscillations.　The　introduction　of　the　Zeeman　magnetic　field　makes　the　system　easier　to　be　applied　as　a　spin　filter.　This　study　provides　theoretical　insights　into　the　realization　of　quantum　computing,　quantum　information　transmission　and　development　of　nanoscale　quantum　devices.　©　2023　World　Scientific　Publishing　Company.