  We systematically investigate the topological properties of spin polarized
Rydberg-dressed fermionic atoms loaded in a bilayer optical lattice. Through
tuning the Rydberg coupling strength and the inter-layer tunneling amplitude,
we identify different types of topological superfluid states generated from the
inter-layer pairing and relative gauge phase modulation of the couples 2D
$p$-wave superfluids. These phases includes gapped/gapless with/without time
reversal symmetry. One of the most interesting states is a gapless paired
topological superfluid with both the time-reversal symmetry and particle-hole
symmetry. This state is equivalent to a topological Kondo lattice model with
the spin-orbit coupling, an in-plane magnetic field, and an additional
particle-hole symmetry. The flexibility of experimental manipulation in such
Rydberg-dressed ferminoic systems therefore becomes a promising system for
realizing interesting topological superfluids.
