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Standard conformal prediction ensures marginal coverage but consistently undercovers underrepresented groups, limiting its reliability for fair uncertainty quantification. Group fairness requires prediction sets to achieve a user-specified coverage level within each protected group. While group-wise conformal inference meets this requirement, it often produces excessively wide prediction sets due to limited sample sizes in underrepresented groups, highlighting a fundamental tradeoff between fairness and efficiency. To bridge this gap, we introduce Surrogate-Assisted Group-Clustered Conformal Inference (SAGCCI), a framework that improves efficiency through two key innovations: (1) clustering protected groups with similar conformal score distributions to enhance precision while maintaining fairness, and (2) deriving an efficient influence function that optimally integrates surrogate outcomes to construct tighter prediction sets. Theoretically, SAGCCI guarantees approximate group-conditional coverage in a doubly robust manner under mild convergence conditions, enabling flexible nuisance model estimation. Empirically, through simulations and an analysis of the phase 3 Moderna COVE COVID-19 vaccine trial, we demonstrate that SAGCCI outperforms existing methods, producing narrower prediction sets while maintaining valid group-conditional coverage, effectively balancing fairness and efficiency in uncertainty quantification.