Recently, as a consequence of the COVID-19 pandemic, dependence on telecommunication for remote learning/working and telemedicine has significantly increased. In this context, preserving high Quality of Service (QoS) and maintaining low latency communication are of paramount importance. Development of an Unmanned Aerial Vehicles (UAV)-aided heterogeneous cellular network is a promising solution to satisfy the aforementioned requirements. There are, however, key challenges ahead, on the one hand, it is challenging to optimally increase content diversity in caching nodes to mitigate the network's traffic over the backhaul. On the other hand is the challenge of attenuated UAVs' signal in indoor environments, which increases users' access delay and UAVs' energy consumption. To address these challenges, we incorporate UAVs, as mobile caching nodes, together with Femto Access points (FAPs) to increase the network's coverage in both indoor and outdoor environments. Referred to as the Cluster-centric and Coded UAV-aided Femtocaching (CCUF) framework, a two-phase clustering framework is proposed for optimal FAPs' formation and UAVs' deployment. The proposed CCUF leads to an increase in the cache diversity, a reduction in the users' access delay, and significant reduction in UAVs' energy consumption. To mitigate the inter-cell interference in edge areas, the Coordinated Multi-Point (CoMP) approach is integrated within the CCUF framework. In contrary to existing works, we analytically compute the optimal number of FAPs in each cluster to increase the cache-hit probability of coded content placement. Furthermore, the optimal number of coded contents to be stored in each caching node is computed to increase the cache-hit-ratio, Signal-to-Interference-plus-Noise Ratio (SINR), and cache diversity and decrease the users' access delay and cache redundancy for different content popularity profiles.