Retrieval-Augmented Generation (RAG) enhances Large Language Models (LLMs) by grounding generation in external knowledge to improve factuality and reduce hallucinations. Yet most deployments assume a centralized corpus, which is infeasible in privacy-aware domains where knowledge remains siloed. This motivates federated RAG (FedRAG), where a central LLM server collaborates with distributed silos without sharing raw documents. In-context RAG violates this requirement by transmitting verbatim documents, whereas parametric RAG encodes documents into light weight adapters that merge with a frozen LLM at inference, avoiding raw-text exchange. We adopt the parametric approach but face two unique challenges induced by FedRAG: high storage and communication from per-document adapters, and destructive aggregation caused by indiscriminately merging multiple adapters. We present FedMosaic, the first federated RAG framework built on parametric adapters. FedMosaic clusters semantically related documents into multi-document adapters with document-specific masks to reduce overhead while preserving specificity, and performs selective adapter aggregation to combine only relevance-aligned, non-conflicting adapters. Experiments show that FedMosaic achieves an average 10.9% higher accuracy than state-of-the-art methods in four categories, while lowering storage costs by 78.8% to 86.3% and communication costs by 91.4%, and never sharing raw documents.