  Monolayer superconducting transition metal dichalcogenide NbSe$_2$ is a
candidate for a nodal topological superconductor by magnetic field. Because of
the so-called Ising spin-orbit coupling that strongly pins the electron spins
to the out-of-plane direction, Cooper pairs in monolayer superconductor
NbSe$_2$ are protected against an applied in-plane magnetic field much larger
than the Pauli limit. In monolayer NbSe$_2$, in addition to the Fermi pockets
at the corners of Brillouin zone with opposite crystal momentum similar to
other semiconducting transition metal dichalcogenides, there is an extra Fermi
pocket around the $\Gamma$ point with much smaller spin splitting, which could
lead to an alternative strategy for pairing possibilities that are manipulable
by a smaller magnetic field. By considering a monolayer NbSe$_2$-ferromagnet
substrate junction, we explore the modified pairing correlations on the pocket
at $\Gamma$ point in hole-doped monolayer NbSe$_2$. The underlying physics is
fascinating as there is a delicate interplay of the induced exchange field and
the Ising spin-orbit coupling. We realize a mixed singlet-triplet
superconductivity, s+f, due to the Ising spin-orbit coupling. Moreover, our
results reveal the admixture state including both odd- and even-frequency
components, associated with the ferromagnetic proximity effect. Different
frequency symmetries of the induced pairing correlations can be realized by
manipulating the magnitude and direction of the induced magnetization.
