This paper introduces a novel approach, evolutionary multi-objective optimisation for fairness-aware self-adjusting memory classifiers, designed to enhance fairness in machine learning algorithms applied to data stream classification. With the growing concern over discrimination in algorithmic decision-making, particularly in dynamic data stream environments, there is a need for methods that ensure fair treatment of individuals across sensitive attributes like race or gender. The proposed approach addresses this challenge by integrating the strengths of the self-adjusting memory K-Nearest-Neighbour algorithm with evolutionary multi-objective optimisation. This combination allows the new approach to efficiently manage concept drift in streaming data and leverage the flexibility of evolutionary multi-objective optimisation to maximise accuracy and minimise discrimination simultaneously. We demonstrate the effectiveness of the proposed approach through extensive experiments on various datasets, comparing its performance against several baseline methods in terms of accuracy and fairness metrics. Our results show that the proposed approach maintains competitive accuracy and significantly reduces discrimination, highlighting its potential as a robust solution for fairness-aware data stream classification. Further analyses also confirm the effectiveness of the strategies to trigger evolutionary multi-objective optimisation and adapt classifiers in the proposed approach.