MOTIVATION: Rare diseases affect millions of people worldwide, yet their genomic foundations remain poorly understood due to limited patient data and strict privacy regulations, such as the General Data Protection Regulation (GDPR) (https://gdpr.eu/tag/gdpr/) in March 2025. These restrictions can hinder the collaborative analysis of genomic data necessary for uncovering disease-causing variants. RESULTS: We present PRISM, a novel privacy-preserving framework based on fully homomorphic encryption (FHE) that facilitates rare disease variant analysis across multiple institutions without exposing sensitive genomic information. To address the challenges of centralized trust, PRISM is built upon a Threshold FHE scheme. This approach decentralizes key management across participating institutions and ensures no single entity can unilaterally decrypt sensitive data. Our method filters disease-causing variants under recessive, dominant, and de novo inheritance models entirely on encrypted data. We propose two algorithmic variants: a multiplication-intensive (MUL-IN) approach and an addition-intensive (ADD-IN) approach. The ADD-IN algorithms minimize the number of costly multiplication operations, enabling up to a 17× improvement in runtime for recessive/dominant filtering and 22× for de novo filtering, compared to MUL-IN methods. While ADD-IN produces larger ciphertexts, efficient parallelization via SIMD and multithreading allows it to handle millions of variants in reasonable time. To the best of our knowledge, this is the first study that utilizes FHE for privacy-preserving rare disease analysis across multiple inheritance models, demonstrating its practicality and scalability in a single-cloud setting. AVAILABILITY AND IMPLEMENTATION: The source code and the data used in this work can be found in https://github.com/mdppml/PRISM.git.