We employed the self-consistent method on a two-orbital type-II time-reversal-symmetric Weyl semimetal, revealing a hybrid pairing of singlet $s$ wave and triplet $p$ wave. We present a detailed analysis of the normal-state electronic structure and the self-consistent results. Our findings indicate that the selection of hybrid pairings is governed by distinct surface Fermi-arc configurations: specifically, $s$-wave pairing dominates on the bottom surface, while $p$-wave pairing prevails on the top. Furthermore, the emergent superconducting state is a second-order topological superconductor with hinge states in the system. Our results identify type-II time-reversal-invariant Weyl semimetals as a promising intrinsic platform for realizing unconventional and topological superconductivity.

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• Fermi surface
• Local density of states
• Surface states
• Topological superconductors
• Bogoliubov-de Gennes equations