Algorithmic fairness is a critical challenge in building trustworthy Machine Learning (ML) models. ML classifiers strive to make predictions that closely match real-world observations (ground truth). However, if the ground truth data itself reflects biases against certain sub-populations, a dilemma arises: prioritize fairness and potentially reduce accuracy, or emphasize accuracy at the expense of fairness. This work proposes a novel training framework that goes beyond achieving high accuracy. Our framework trains a classifier to not only deliver optimal predictions but also to identify potential fairness risks associated with each prediction. To do so, we specify a dual-labeling strategy where the second label contains a per-prediction fairness evaluation, referred to as an unfairness risk evaluation. In addition, we identify a subset of samples as highly vulnerable to group-unfair classifiers. Our experiments demonstrate that our classifiers attain optimal accuracy levels on both the Adult-Census-Income and Compas-Recidivism datasets. Moreover, they identify unfair predictions with nearly 75% accuracy at the cost of expanding the size of the classifier by a mere 45%.