On-policy reinforcement learning has become the dominant paradigm for reasoning alignment in large language models, yet its sparse, outcome-level rewards make token-level credit assignment notoriously difficult. On-Policy Distillation (OPD) alleviates this by introducing dense, token-level KL supervision from a teacher model, but typically applies this supervision uniformly across all rollouts, ignoring fundamental differences in signal quality. We propose **S**ignal-**C**alibrated **O**n-**P**olicy Distillation **E**nhancement (**SCOPE**), a dual-path adaptive training framework that routes on-policy rollouts by correctness into two complementary supervision paths. For incorrect trajectories, SCOPE performs teacher-perplexity-weighted KL distillation to prioritize instances where the teacher demonstrates genuine corrective capability, while down-weighting unreliable guidance. For correct trajectories, it applies student-perplexity-weighted Maximum Likelihood Estimation to concentrate reinforcement on low-confidence samples at the capability boundary rather than over-reinforcing already mastered ones. Both paths employ a group-level normalization to adaptively calibrate weight distributions, accounting for the intrinsic difficulty variance across prompts. Extensive experiments on six mathematical reasoning benchmarks show that SCOPE achieves average relative improvements of 11.42% in Avg@32 and 7.30% in Pass@32 over competitive baselines, with extended experiments demonstrating its broader applicability. Code is available at [https://github.com/machine981/SCOPE](https://github.com/machine981/SCOPE).