Distributed data-centric systems, such as Named Data Networking, utilize in-network caching to reduce application latency by buffering relevant data in high-speed memory. However, the significant increase in data traffic makes expanding memory capacity prohibitively expensive. To address this challenge, integrating technologies like non-volatile memory and high-speed solid-state drives with dynamic random-access memory can form a cost-effective multi-tier cache system. Additionally, most existing caching policies focus on categorizing data based on recency and frequency, overlooking the varying Quality-of-Service (QoS) requirements of applications and customers—a concept supported by Service Level Agreements in various service delivery models, particularly in Cloud computing. One of the most prominent algorithms in caching policy literature is the Adaptive Replacement Cache (ARC), that uses recency and frequency lists but does not account for QoS. In this paper, we propose a QoS-aware Multi-tier Adaptive Replacement Cache (QM-ARC) policy. QM-ARC extends ARC by incorporating QoS-based priorities between data applications and customers using a penalty concept borrowed from service-level management practices. QM-ARC is generic, applicable to any number of cache tiers, and can accommodate various penalty functions. Furthermore, we introduce a complementary feature for QM-ARC that employs Q-learning to dynamically adjust the sizes of the two ARC lists. Our solution, evaluated using both synthetic and real-world traces, demonstrates significant improvements in QoS compared to state-of-the-art methods by better considering priority levels. Results show that QM-ARC reduces penalties by up to 45% and increases the hit rate for high priority data by up to 84%, without negatively impacting the overall hit rate, which also increases by up to 61%