<p>Binary classification tasks with imbalanced classes pose significant challenges in machine learning. Traditional classifiers often struggle to accurately capture the characteristics of the minority class, resulting in biased models with subpar predictive performance. In this paper, we introduce a novel approach to tackle this issue by leveraging Universum points to support the minority class within quadratic twin support vector machine models. Unlike traditional classifiers, our models utilize quadratic surfaces instead of hyperplanes for binary classification, providing greater flexibility in modeling complex decision boundaries. By incorporating Universum points, our approach enhances classification accuracy and generalization performance on imbalanced datasets. We generated four artificial datasets to demonstrate the flexibility of the proposed methods. Additionally, we validated the effectiveness of our approach through empirical evaluations on benchmark datasets, demonstrating superior performance compared to conventional classifiers and existing methods for imbalanced classification.</p>