Recently, cross-attention-based contextual automatic speech recognition (ASR) models have made notable advancements in recognizing personalized biasing phrases. However, the effectiveness of cross-attention is affected by variations in biasing information volume, especially when the length of the biasing list increases significantly. We find that, regardless of the length of the biasing list, only a limited amount of biasing information is most relevant to a specific ASR intermediate representation. Therefore, by identifying and integrating the most relevant biasing information rather than the entire biasing list, we can alleviate the effects of variations in biasing information volume for contextual ASR. To this end, we propose a purified semantic correlation joint modeling (PSC-Joint) approach. In PSC-Joint, we define and calculate three semantic correlations between the ASR intermediate representations and biasing information from coarse to fine: list-level, phrase-level, and token-level. Then, the three correlations are jointly modeled to produce their intersection, so that the most relevant biasing information across various granularities is highlighted and integrated for contextual recognition. In addition, to reduce the computational cost introduced by the joint modeling of three semantic correlations, we also propose a purification mechanism based on a grouped-and-competitive strategy to filter out irrelevant biasing phrases. Compared with baselines, our PSC-Joint approach achieves average relative F1 score improvements of up to 21.34% on AISHELL-1 and 28.46% on KeSpeech, across biasing lists of varying lengths.