  The large lattice constant of Moire superlattice formed in twisted bilayer
graphene for small twist enables observing the Landau levels splitting into
Hofstadter butterflies in energy spectra for moderate magnetic field. This is
expected for generic system under homogeneous bias conditions but its
robustness against spatial potential fluctuations is left open question. We
study the energy structure of twisted bilayer system in dependence of both, the
homogeneous magnetic field and the bias voltage applied exclusively in its
central part. Although the translational symmetry is broken, the energy states
mainly localized outside the central region may still condense on Landau levels
and these would split revealing self-similarity feature. Moreover, besides the
generic branch of energy states with zero-mode Landau level at charge
neutrality point, when both layers are biased with the same voltage, the second
look-alike energy branch shifted upwards can be developed by states largely
localized in central region. Otherwise, for counter-biasing of layers, only
generic branch exists but with lowest Landau layers flanked by either,
hole-like and electron-like states localized at the top or at the bottom layer
of central biased part of twisted bilayer system.
