The integration of AI-powered tutoring in higher education presents a transformative opportunity to enhance student engagement and learning outcomes. AI-generated data provides insights into student interaction patterns and learning preferences; however, studies on optimising AI tools for improved educational outcomes remain limited. This study addresses this gap by analysing student engagement with an AI Teaching Assistant in accounting (ACC), economics (ECO), and law (LAW) subjects. Using the Community of Inquiry (CoI) Framework, which highlights cognitive, teaching, and social presence in learning, this study examines how AI tutors support student engagement and self-directed learning. Student interaction logs from the AI Tutoring dashboard in the university's Canvas LMS were analysed through frequency distribution and content analysis. Findings indicate that ACC students primarily use the AI Tutor for practical applications, concept reinforcement, and exam preparation, reflecting the applied nature of accounting. In ECO, engagement focuses on problem-solving, while LAW students predominantly seek conceptual clarification, highlighting the AI Tutor's role in supporting legal education. These results highlighted AI tutors' potential to provide personalised learning, facilitate on-demand explanations, and enhance academic support. By offering empirical evidence on AI engagement patterns across disciplines, this study fills a critical research gap and provides recommendations for improving AI-powered tutoring, ensuring its adaptability to different disciplines and learning needs. Grounded in the CoI framework, these insights contribute to the growing discourse on AI integration in education, promoting effective and engaging digital learning environments.