Fairness in machine learning has become a critical concern. Existing approaches often focus on achieving full fairness across all score ranges generated by predictive models, ensuring fairness in both high- and low-percentile populations. However, this stringent requirement can compromise predictive performance and may not align with the practical fairness concerns of stakeholders. In this work, we propose a novel framework for building partially fair machine learning models that enforce fairness only within a specific percentile interval of interest while maintaining flexibility in other regions. We introduce statistical metrics to evaluate partial fairness within a given percentile interval. To achieve partial fairness, we propose an in-processing method by formulating the model training problem as constrained optimization with difference-of-convex constraints, which can be solved by an inexact difference-of-convex algorithm (IDCA). We provide the complexity analysis of IDCA for finding a nearly KKT point. Through numerical experiments on real-world datasets, we demonstrate that our framework achieves high predictive performance while enforcing partial fairness where it matters most.