  We study constructions and classifications of three-generation models based
on magnetized $T^4$ and $T^4/{Z}_2$ orbifold as candidates of the compact
space. We focus on chiral fermion zero-mode wave functions in the extra
dimensions. Freedoms of constant gauge fields, called Scherk-Schwarz phases are
taken into account. Infinite number of three-generation models are yielded,
corresponding to the ways in which the magnetic flux can be turned on. We
classify them in a systematic manner, clarifying the relationship between
different models. The Higgs sector is also studied by analyzing possible
assignments of the magnetic flux and Scherk-Schwarz phases, etc. to left- and
right-handed fermions.
