We investigate quantum entanglement and coherence for four classes of Bell-like fermionic states in the vicinity of the event horizon of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. Contrary to the common expectation that maximally entangled states always provide superior quantum resources, our results show that their entanglement can be lower than that of suitably chosen non-maximally entangled states in this curved spacetime background. This reveals that non-maximally entangled st