Longitudinal electronic health records (EHRs) capture years of patient history across notes, codes, labs, and procedures, and contain evidence needed to reason about likely clinical outcomes. However, comprehensive clinician review of these records is impractical, and LLM-based processing is costly and often unreliable, missing some relevant observations while hallucinating others. We therefore propose **EviGen**, a three-layer framework for verifiable clinical rationale generation that addresses these challenges. The **first layer** is a patient-conditioned retriever that uses learnable queries to find evidence predictive of, not just textually relevant to, a clinical outcome and ranks it by prediction attribution scores. The **second layer** is an LLM generator that consumes this ranked evidence as a scaffold to produce a clinical rationale grounded in the retrieved spans. The **third layer** is a process-supervised verifier that checks the generated rationale at the reasoning-step level, flagging unreliable claims. Across three medical prediction datasets, EviGen improves prediction performance and rationale faithfulness over full-context LLM and RAG baselines, and is preferred by clinical reviewers in a usability evaluation.