  Unconventional fermions with high degeneracies in three dimensions beyond
Weyl and Dirac fermions have sparked tremendous interest in condensed matter
physics. Here, we study quantum Hall effects (QHEs) in a two-dimensional (2D)
unconventional fermion system with a pair of gapped spin-1 fermions. We find
that the original unlimited number of zero energy Landau levels (LLs) in the
gapless case develop into a series of bands, leading to a novel QHE phenomenon
that the Hall conductance first decreases (or increases) to zero and then
revives as an infinite ladder of fine staircase when the Fermi surface is moved
toward zero energy, and it suddenly reverses with its sign being flipped due to
a Van Hove singularity when the Fermi surface is moved across zero. We further
investigate the peculiar QHEs in a dice model with a pair of spin-1 fermions,
which agree well with the results of the continuous model.
