Deep learning (DL) systems, though being widely used, still suffer from quality and reliability issues. Researchers have put many efforts to investigate these issues. One promising direction is to leverage uncertainty, an intrinsic characteristic of DL systems when making decisions, to better understand their erroneous behavior. DL system testing is an effective method to reveal potential defects before the deployment into safety- and security-critical applications. Various techniques and criteria have been designed to generate defect-triggers, i.e. adversarial examples (AEs). However, whether these test inputs could achieve a full spectrum examination of DL systems remains unknown and there still lacks understanding of the relation between AEs and DL uncertainty. In this work, we first conduct an empirical study to uncover the characteristics of AEs from the perspective of uncertainty. Then, we propose a novel approach to generate unique inputs that are missed by existing techniques. The generated data are demonstrated to be more effective in revealing defects even for DL systems equipped with defense mechanism. Further, we investigate the usefulness and effectiveness of the data for DL robustness enhancement.