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Motivated by recent tunneling experiments on superconducting gated MoS₂, we propose a spin-triplet Ising pairing phase of the system, which is a triplet nodal superconductor characterized by the V shape density of states in the low energy. In the triplet Ising pairing phase, the calculated bulk density of states agree well with the experimental results. In the armchair edge, the nodal phase supports flat bands with a large number of zero energy modes and they would result in a large zero-bias conductance peak in the tunneling experiments. Moreover, the in-plane upper critical field in the triplet Ising pairing phase is systematically studied and the experimental data are consistently explained.