<p>The rise of e-business, cloud computing, and digital services has led to a significant increase in the number of publicly available APIs, often offering overlapping functionalities. In this increasingly competitive landscape, service selection is no longer driven solely by functionality, but also by cost-effectiveness and compliance with usage constraints. This paper addresses the problem of API service selection under budget limitations, aiming to maximize the total number of allowed API calls within a fixed time period. We first formalize this selection problem and propose algorithmic solutions, including two greedy heuristics and an exact dynamic programming (DP) approach. While the greedy methods offer high computational efficiency, the DP-based solution guarantees optimal selection under the given constraints. To address the potential overuse of certain services and the underuse of others, we introduce a fairness-aware selection mechanism designed to promote a more balanced distribution of service invocations. This mechanism encourages the inclusion of underutilized services, improving long-term sustainability and diversity in service utilization. We validate our proposals through extensive experiments, demonstrating their effectiveness in terms of total API calls, execution time, and fairness of service utilization.</p>