We propose an approach to train a fair cost-based abstain option classifier. Existing literature on fairness in classification with abstention is limited, covering only coverage-based abstention models. In coverage-based abstention models, the target coverage is decided beforehand and is kept the same for all the groups. In contrast, cost-based approaches introduce a cost for abstention, which can cause uneven abstention rates between different groups, leading to an unfair system. We extend the independence and separation fairness criteria to consider abstention. We provide a model-agnostic in-processing algorithm to incorporate these constraints in the models. We demonstrate the algorithm’s efficacy by experimenting with two different cost-based abstain option classifiers. Additionally, we explore mixing constraints from independence and separation criteria into one model, which is impossible in a binary classification task.