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This study draws on appraisal theory to examine the antecedents of student engagement in GenAI-supported learning. Specifically, it investigates how GenAI competency, academic self-efficacy, perceived ease of use (PE), perceived usefulness (PU), and emotion interact to shape engagement. Using a repeated measures design, data were collected from 45 postgraduate students across ten learning sessions, yielding 321 valid responses. Structural equation modelling and bootstrapped mediation analyses were employed. Results highlight GenAI competency as the strongest predictor of engagement. Emotion emerged as a critical mediator, fully mediating the relationship between PU and engagement, while PU also fully mediated the link between PE and engagement. In contrast, academic self-efficacy was not significantly related to engagement.