Due to noise, redundancy and uncertainty with respect to predictive confidence, proper classification of high-dimensional biological data remains a significant challenge. To overcome these shortcomings, this paper proposes a High-Confidence Residual Hybrid Ensemble (HCRHE) Network, which is a composite of residual learning, deep neural modelling, and confidence-conscious decision fusion to classify diseases with high confidence. The Cancer Genome Atlas (TCGA) contains large-scale data on DNA methylation that are susceptible to overfitting and unstable forecasts by using conventional deep learning models to evaluate the proposed methodology. To learn latent patterns due to reconstruction, HC-RHE architecture consists of a primary-prediction base multilayer perceptron (MLP), together with a residual learning path that is constructed using an autoencoder and residual MLP. A new machine called a confidence-based fusion technique allows the dynamical weighting of the base and residual prediction in terms of model certainty and makes adaptive decision-making. Also, forecasts with high confidence margins are retained and a high-confidence filtering process used, which maximizes reliability with minimal coverage loss. An accuracy-optimized threshold selection strategy is also provided in order to enhance the performance of classification further. Vast comparative experiments are conducted with the state-of-the-art deep learning baselines, including CNN, autoencoder-based classifiers, Dense DropConnect, residual CNN frameworks, and Basic MLP (Adam and SGD). The proposed HC-RHE has a much better accuracy at 98.7 compared to all other methods. These results prove success of confidence-aware residual fusion as they reflect continuous improvement over the best baseline CNN model. The proposed framework is, all in all, exceptionally promising to the field of clinical decision-support systems and gives a credible, intuitive, and high-confidence classification paradigm of high-dimensional biomedical data.