With the expansion of business scales and scopes on online platforms, multi-scenario matching has become a mainstream solution to reduce maintenance costs and alleviate data sparsity. The key to effective multi-scenario recommendation lies in capturing both user preferences shared across all scenarios and scenario-aware preferences specific to each scenario. However, existing methods often overlook user-specific modeling, limiting the generation of personalized user representations. To address this, we propose PERSCEN, an innovative approach that incorporates user-specific modeling into multi-scenario matching. PERSCEN constructs a user-specific feature graph based on user characteristics and employs a lightweight graph neural network to capture higher-order interaction patterns, enabling personalized extraction of preferences shared across scenarios. Additionally, we leverage vector quantization techniques to distil scenario-aware preferences from users' behavior sequence within individual scenarios, facilitating user-specific and scenario-aware preference modeling. To enhance efficient and flexible information transfer, we introduce a progressive scenario-aware gated linear unit that allows fine-grained, low-latency fusion. Extensive experiments demonstrate that PERSCEN outperforms existing methods. Further efficiency analysis confirms that PERSCEN effectively balances performance with computational cost, ensuring its practicality for real-world industrial systems.