Medication recommendation must combine patient-specific treatment evidence with the interaction structure of a prescription. The central challenge is to determine which evidence supports each medication and how strongly to regularize interactions while preserving predictive quality. We propose EviDrug, a clinical evidence-guided residual learning framework. Its clinical-memory backbone integrates a self-trained visit-aware encoder, training-case memory and one medication-set interaction block to establish a patient-specific prescription. A gated refinement head combines the backbone states with clinical associations and history-conditioned medication identities through bounded logit corrections. Drug-drug interaction (DDI) feedback adapts regularization strength using training-query predictions. Across MIMIC-IV, NWICU and SICdb, EviDrug leads twelve published-method baselines in AP, F1 and Jaccard, improving AP by 2.26, 2.06 and 1.71 percentage points over the strongest comparator. These gains come at lower parameter and runtime costs than MetaDrug. Matched controls demonstrate DDI reductions with stable predictive quality. Code is available at https://github.com/LIZESHENG13/EviDrug.

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