  The study of exotic superconductivity in two dimensions has been a central
theme in solid state and materials research communities. Experimentally
exploring and identifying new fascinating interface superconductors with a high
transition temperature ($T_c$) is challenging. Here, we report an experimental
observation of intriguing two-dimensional superconductivity with a $T_c$ up to
3.8 K at the interface between Mott insulator Ti$_2$O$_3$ and polar
semiconductor GaN. At the verge of superconductivity, we also observe a
striking quantum metallic-like state, demonstrating that it is a precursor to
the two-dimensional superconductivity as the temperature is decreased. Our work
is the first time finding this intriguing superconducting state at the
heterointerface, which not only brings a new broad of perspective on the
emergent quantum phenomena at the heterointerfaces but also sheds new light on
exploiting the novel heterointerface superconductivity with high-$T_c$ via
heterostructure engineering.
