  We present two band models for free fermion with charge conjugation symmetry
in three dimensions. Without time reversal symmetry (TRS), the weak pairing
gapless $A$-phase is a Majorana fermion $p_x+ip_y$ wave FFLO state while the
strong pairing gapped $B$-phase belongs to topologically trivial Class $D$.
With TRS, there is a Majorana fermion $B$-phase belonging to Class $DIII$ with
a non-zero Hopf invariant. The TRS $A$-phase is also a Majorana fermion FFLO
state with TRS. The surface states of the TRS $B$-phase are either a
valley-momentum locked Majorana-Dirac cone or a linear-quadratic mixed cone for
a specific surface. The surface states of the $A$-phase on one surface are
topologically nontrivial, either having $\mathbb{Z}$ or $\mathbb{Z}_2$
invariant depending on whether the system is TRS or not. The edge states of
that surface are gapless Majorana modes. The Majorana fermion gapless FFLO
states can be realized in critical Weyl semimetals (WSM) in which dual single
Weyl nodes form dipoles and are nearly annihilated. The gapped $B$-phase
emerges when Weyl node dipoles are about to be created. The WSM TaAs-family, a
type-II WSM series Mo$_x$W$_{1-x}$Te$_2$-family, possible WSM La/LuBi$_{1-x}$
Sb$_x$Te$_3$ and topological crystalline insulators Sn$_{1-x}$Pb$_x$(Te,Se) are
candidates to be manipulated into these critical states based on Majorana
fermion models.
