Uncertainty quantification (UQ) is essential for improving the reliability of large language models (LLMs). However, multi-sample UQ methods typically employ a fixed sampling budget for all queries, leading to computational redundancy. In addition, multi-sample UQ methods often fail in the presence of consistent errors. To address these limitations, we propose CASE (Contradiction-aware Adaptive Spectral and Entropic UQ), a UQ framework that jointly models semantic disagreement and token-level uncertainty under an adaptive sampling paradigm. Specifically, CASE constructs a contradiction graph over sampled responses and quantifies semantic disagreement using normalized spectral norms of the graph representation. The resulting uncertainty signals are further leveraged for adaptive sampling, enabling query-dependent budget allocation while reducing redundant computation. In addition, CASE incorporates token-level predictive entropy as a complementary uncertainty signal to mitigate the failure of graph structures under consistent errors. Experimental results demonstrate that CASE outperforms existing multi-sample UQ methods across factual question answering datasets while reducing sampling costs by over 30% on average.