Algorithmic discrimination occurs when technological systems do not treat users fairly based on identity, demographics, or other personal characteristics. This study contributes towards understanding the diversity and inclusion of different demographic groups in Responsible healthcare AI systems. The impact of socio-economic discrimination in healthcare diagnosis, health planning, and patient care management tasks is analyzed through research articles published between 2019 and 2025. We aim to highlight the significance of fairness within AI-based healthcare systems. Our research methodology and research questions are based on these conducted studies, which also leads to defining our search strategy, selection process, data analysis, and extraction. From theoretical concerns about AI bias in 2019 to empirical evidence of real-world discrimination and mitigation efforts in 2025, our analysis reveals that there is a dire need for the entire research community to address algorithmic discrimination and promote trustworthiness and responsibility in AI systems for healthcare, which, if not taken care of, can lead to catastrophic outcomes for the overall health sector and the society.