High attrition/dropout rates and low engagement have been major concerns of online educators. This study examined female high school students' cognitive engagement and disengagement in an online learning context during the COVID-19 pandemic through the lens of self-determination theory's basic psychological needs. We investigated an extended dual-process motivation mediation model that emphasizes the mediating role of the need for competence, including an additional factor, technology self-efficacy, in a South Korean high school context (n = 235). Results from structural equation modelling provided evidence for the proposed model. Our findings indicated that the exogenous variables (ie, perceived autonomy support, perceived teacher control and technology self-efficacy) predicted cognitive engagement and disengagement with the mediating role of competence need satisfaction and competence need frustration. We found distinct processes including (a) "autonomy support-competence need satisfaction-cognitive engagement", (b) "teacher control-competence need frustration-cognitive disengagement", (c) "technology self-efficacy-competence need satisfaction-cognitive engagement" and (d) "technology self-efficacy-competence need frustration (negative effect)-cognitive disengagement". This study suggests using autonomy support strategies to fulfil students' competence needs in online learning contexts. We also found a possible role of technology self-efficacy in influencing psychological competence needs, cognitive engagement and cognitive disengagement in online learning contexts. Implications of the findings are discussed.