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We report our point-contact spectroscopy (PCS) study on the superconductingstate of the type-II Dirac semimetal PdTe$_2$ with a superconducting transitiontemperature $T\rm_c \sim$ 1.65 K. Both mechanical- and soft- PCS differentialconductance curves at 0.3 K show a consistent double-peak structure and theycan be perfectly fitted by a single s-wave gap based on theBlonder-Tinkham-Klapwijk model. The gap follows a typicalBardeen-Cooper-Schrieffer temperature behavior, yielding $\Delta_0 \sim$ 0.29meV and 2$\Delta_0$/$k\rm_{B}$$T\rm_{c}$ = 4.15 in the strong coupling regime.A sudden suppression of the superconducting gap in magnetic field around$H{\rm_{c1}}$ $\sim$ 130 Oe is observed for most point-contacts on PdTe$_2$,characteristic of a first-order transition for type-I superconductor in field.However, for other contacts, a smooth evolution of the PCS conductance persistsup to $H{\rm_{c2}}$ $\sim$ 600 Oe, signaling a local type-II superconductivity.The observed admixture of type-I and type-II superconductivity can possiblyarise from an inhomogeneous electron mean free path on the surface of PdTe$_2$due to its topological surface states.

Single full gap with mixed type-I and type-II superconductivity on surface of the type-II Dirac semimetal PdTe2 by point-contact spectroscopy