Rapid financial innovation has been accompanied by a sharp increase in patenting activity, making timely and comprehensive prior-art discovery more difficult. This problem is especially evident in financial technologies, where innovations develop quickly, patent collections grow continuously, and citation recommendation systems must be updated as new applications arrive. Existing patent retrieval and citation recommendation methods typically rely on static indexes or periodic retraining, which limits their ability to operate effectively in such dynamic settings. In this study, we propose a real-time patent citation recommendation framework designed for large and fast-changing financial patent corpora. Using a dataset of 428,843 financial patents granted by the China National Intellectual Property Administration (CNIPA) between 2000 and 2024, we build a three-stage recommendation pipeline. The pipeline uses large language model (LLM) embeddings to represent the semantic content of patent abstracts, applies efficient approximate nearest-neighbor search to construct a manageable candidate set, and ranks candidates by semantic similarity to produce top-k citation recommendations. In addition to improving recommendation accuracy, the proposed framework directly addresses the dynamic nature of patent systems. By using an incremental indexing strategy based on hierarchical navigable small-world (HNSW) graphs, newly issued patents can be added without rebuilding the entire index. A rolling day-by-day update experiment shows that incremental updating improves recall while substantially reducing computational cost compared with rebuild-based indexing. The proposed method also consistently outperforms traditional text-based baselines and alternative nearest-neighbor retrieval approaches.