This paper describes the system submitted by Papago team for the quality estimation task at WMT 2020. It proposes two key strategies for quality estimation: (1) task-specific pretraining scheme, and (2) task-specific data augmentation. The former focuses on devising learning signals for pretraining that are closely related to the downstream task. We also present data augmentation techniques that simulate the varying levels of errors that the downstream dataset may contain. Thus, our PATQUEST models are exposed to erroneous translations in both stages of task-specific pretraining and finetuning, effectively enhancing their generalization capability. Our submitted models achieve significant improvement over the baselines for Task 1 (Sentence-Level Direct Assessment; EN-DE only), and Task 3 (Document-Level Score).