Deep learning based methods have become a paradigm for cover song identification (CSI) in recent years, where the ByteCover systems have achieved state-of-the-art results on all the mainstream datasets of CSI. However, with the burgeon of short videos, many real-world applications require matching short music excerpts to full-length music tracks in the database, which is still under-explored and waiting for an industrial-level solution. In this paper, we upgrade the previous ByteCover systems to ByteCover3 that utilizes local features to further improve the identification performance of short music queries. ByteCover3 is designed with a local alignment loss (LAL) module and a two-stage feature retrieval pipeline, allowing the system to perform CSI in a more precise and efficient way. We evaluated ByteCover3 on multiple datasets with different benchmark settings, where ByteCover3 beat all the compared methods including its previous versions.