ABSTRACT Illegitimate tasks are duties that violate established role expectations, such as assigning urban planning officers to manage traffic hotlines. In the public sector, bureaucratic structures, resource constraints, and leadership limitations often contribute to the proliferation of such tasks, yet their impact on public servants' behaviors remains unclear. This study examines how and when illegitimate tasks inhibit public servants' innovative work behavior through the mediating role of cognitive flexibility and the moderating roles of different forms of trust in leaders. Hierarchical model analyses using multi‐wave data from public servants and their managers in Vietnam reveal that illegitimate tasks indirectly reduce innovative work behavior via cognitive flexibility. Additionally, relationship‐based trust amplifies the negative effect of illegitimate tasks on cognitive flexibility, whereas character‐based trust does not. These findings highlight the need to minimize illegitimate task assignments and reveal the potential drawbacks of relationship‐based trust in such adverse work conditions.