We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases T2/Z3, T2/Z4 and T2/Z6. We can obtain the exact and analytical results which can be applicable for any larger values of the quantized magnetic flux M, and show that the (non-diagonalized) kinetic terms are generated via our formalism and the number of the surviving physical states are calculable in a rigorous manner by simply following usual procedures in linear algebra in any case. Our approach is very powerful when we try to examine properties of the physical states on (complicated) magnetized orbifolds T2/Z3, T2/Z4, T2/Z6 (and would be in other cases on higher-dimensional torus) and could be an essential tool for actual realistic model construction based on these geometries. (Note: This article is registered under preprint number: arXiv:1409.5421.). © 2014 The Authors.