Data sovereignty has become a central concern in public-sector digital transformation, particularly with the rise of data-intensive technologies such as Generative Artificial Intelligence (GenAI). However, existing research has primarily focused on conceptual and regulatory dimensions, with limited empirical insight into how sovereignty shapes technology adoption in practice. This study examines how data sovereignty influences the adoption and use of GenAI in the public sector. Drawing on a qualitative case study based on 19 interviews across national governance and service delivery contexts, the findings show that data sovereignty operates as a socio-technical condition shaping organisational decision-making. It constrains implementation pathways and generates tensions related to control, compliance, infrastructure, and strategic autonomy. These findings shift the understanding of data sovereignty from a policy concern to an organisationally enacted condition that structures digital innovation. The study contributes to research on AI governance by demonstrating how sovereignty is operationalised in practice and how it shapes public-sector GenAI adoption in resource-constrained contexts.