This study introduces a novel application of Quantum Generative Adversarial Networks (QGANs) by incorporating a new fairness principle, \textit{representational fairness}, which improves equitable representation of various demographic groups in quantum-generated data. We propose a \textit{group-wise} gradient norm clipping technique that constrains the magnitude of discriminator updates for each demographic group, thereby promoting fair data generation. Furthermore, our approach mitigates the issue of mode collapse, which is inherent in both QGANs and classical GANs. Empirical evaluations confirm that this method enhances \textit{representational fairness} while maintaining high-quality sample generation.