We propose a Byzantine-resilient federated conformal prediction (FCP) method that leverages partial model sharing, where only a subset of model parameters is exchanged each round. Unlike existing robust FCP approaches that primarily harden the calibration stage, our method protects both the federated training and conformal calibration phases. During training, partial sharing inherently restricts the attack surface and attenuates poisoned updates while reducing communication. During calibration, clients compress their non-conformity scores into histogram-based characterization vectors, enabling the server to detect Byzantine clients via distance-based maliciousness scores and to estimate the conformal quantile using only benign contributors. Experiments across diverse Byzantine attack scenarios show that the proposed method achieves closer-to-nominal coverage with substantially tighter prediction intervals than standard FCP, establishing a robust and communication-efficient approach to federated uncertainty quantification.