Hypergraphs serve as a powerful tool for modeling complex relationships across domains like social networks, transactions, and recommendation systems. The (k,g)-core model effectively identifies cohesive subgraphs by assessing internal connections and co-occurrence patterns, but it is susceptible to inflated cohesiveness due to trivial hyperedges. To address this, we propose the $(k,g,p)$-core model, which incorporates the relative importance of hyperedges for more accurate subgraph detection. We develop both Naïve and Advanced pruning algorithms, demonstrating through extensive experiments that our approach reduces the execution frequency of costly operations by 51.9% on real-world datasets.