Magnetic skyrmions are spin topological textures of potential interest in spintronics-related data storage and processing devices. Here, we show the emergence of unconventional skyrmions in a geometrically frustrated triangular lattice on an inversion-symmetry-breaking two-dimensional electron gas substrate. Starting with a classical double-exchange mechanism, this generic interface induces exotic skyrmionic and unique noncoplanar magnetic states not observed in the equivalent square lattice interface. We study the model by deriving an effective spin Hamiltonian. Large scale classical Monte Carlo simulations provide a quantitative evidence for the emergence of these exotic magnetic states. We found that these chiral magnetic states exhibit a substantial and nonzero topological Hall conductivity. As potential material candidates, we propose Cr/MoS2, Fe/MoS2, and Fe/WSe2 interfaces because they have the requisite underlying triangular lattice structures and large spin-orbit coupling.