  The electronic state of \alpha-type organic Dirac fermion systems such as
\alpha-(ET)_2I_3 or \alpha-(BETS)_2I_3 has been studied under magnetic fields
using the four-band tight-binding model with Peierls phase factors. The
validity of the Dirac fermion picture in these materials was confirmed by the
generated Hofstadter butterfly and its Chern numbers. The four-component
envelope function of the N = 0 Landau level with valley degeneracy was studied.
It was found that the two degenerate valley states have different weights on A
and A' molecules connected by inversion. This feature is also recognized for
the N = 0 spin-split Landau levels under the Zeeman effect and the spin-orbit
interaction. The spontaneous valley symmetry breaking in the N = 0 Landau
levels due to the exchange interaction results in the \nu = 1 and -1 quantum
Hall states accompanied by the spatial charge and spin modulations in a unit
cell.
