Experimental design is critical for evidence-based decision-making in healthcare, marketing, and public policy. However, designing efficient experiments across heterogeneous subgroups presents significant challenges. Existing methods often optimize for statistical power or overall sample efficiency, overlooking crucial fairness considerations across these different subgroups. To address this gap, we introduce a Fairness-Aware Contextual Track-and-Stop Design (F-CTSD) algorithm. The proposed F-CTSD algorithm provides statistical guarantees on subgroup fairness while minimizing required sample sizes. We quantify the fairness-efficiency trade-off and derive the sample complexity bound for the proposed F-CTSD algorithm under its fairness constraints. We further theoretically prove that the proposed F-CTSD algorithm consistently produces accurate treatment effect estimates even under fairness requirements, enhancing statistical reliability. Numerical experiments show that the proposed F-CTSD algorithm outperforms existing methods, achieving higher sample efficiency while reducing subgroup fairness violations by 4.95%.