The rapid proliferation of Artificial Intelligence (AI), algorithmic governance, and machine learning (ML) frameworks is fundamentally restructuring modern public administration. While these technologies offer unprecedented operational efficiencies, automated decision-making introduces profound ethical, legal, and epistemological challenges across administrative hierarchies. Objective: This systematic review evaluates the multi-dimensional impact of AI and algorithmic governance on modern public administration, focusing on algorithmic fairness in human resource management (HRM), judicial procedural justice, electoral security, public health policy, and digital public infrastructure (DPI).Methods: Following Scopus Qq systematic review protocols, literature was gathered and synthesized across 12 issues of the British Journal of Contemporary Research (BJCR Vol. 1, Issues 1-5) and the British Journal of Advanced Research (BJAR Vol. 1, Issues 1-4). The study applies an epistemological incongruence framework and multi-metric performance analysis to evaluate administrative AI deployments. Results: Algorithmic decision-making significantly enhances operational velocity and data processing capacity in public administrative settings (e.g., enhanced XGBoost anomaly detection achieving 91.5% F1-score; multi-modal explainable frameworks reaching 93.8% accuracy). However, uncorrected AI models introduce systemic epistemological incongruence, wherein statistical proxies substitute human context, exacerbating bias in workforce recruitment and public sector resource allocation. Furthermore, generative AI and synthetic media pose severe challenges to electoral integrity, necessitating automated epistemic sifting architectures (such as the CHARLES model).Conclusion: Public sector AI integration requires a paradigm shift from ad hoc technological adoption to institutionalized, explainable, and human-centric governance frameworks. Policy recommendations emphasize mandatory algorithmic impact audits, hybrid human-in-the-loop decision structures, and cross-border digital trust standards.