Q-rung orthopair hesitant fuzzy set (q-ROHFS) is a powerful instrument for addressing uncertainty problems. Nevertheless, the classification methods of three-way multi-attribute group decision-making (TWD-MAGDM) under this new model have been seldom researched, and the current TWD-MAGDM method in a hesitant fuzzy environment fails to consider the psychological behavior and fuzzy correlation of decision-maker, resulting in not enough distinction among classified objects. To resolve this issue, we present a novel TWD-MAGDM classification model for a q-rung orthopair hesitant fuzzy (q-ROHF) environment. Firstly, this paper considers the fuzzy correlation by allocating weight through Shapely and combines the prospect theory and Gaussian function to develop a preference function that can accurately describe the loss and gain. Based on this function, it presents a relative utility function that can more accurately measure the utility. Secondly, we provide a conditional probability that considers psychological factors and has enhanced recognition capabilities. Finally, a novel TWD-MAGDM classification model for q-ROHF is provided based on the new relative utility function and conditional probabilities. We subsequently verify the efficacy of the proposed approach.