  Type-II Dirac semimetals (DSMs) have a distinct Fermi surface topology, which
allows them to host novel topological superconductivity (TSC) different from
type-I DSMs. Depending on the relationship between intra- and inter-orbital
electron-electron interactions, the phase diagram of superconductivity is
obtained in type-II DSMs. We find that when the inter-orbital attraction is
dominant, an unconventional inter-orbital intra-spin superconducting (SC) state
($B_{1u}$ and $B_{2u}$ pairing channels of $D_{4h}$ point group) is realized,
yielding hybrid TSC, i.e., first- and second-order TSC exists at the same time.
Further analysis reveals the Majorana flat bands on the $z$-directed hinges,
which penetrate through the whole hinge Brillouin zone and link the projections
of the surface helical Majorana cones at time-reversal-invariant momenta. These
higher-order hinge modes are symmetry-protected and can even host strong
stability against finite $C_{4z}$ rotation symmetry-breaking order. We suggest
that experimental realization of these findings can be explored in transition
metal dichalcogenides.
