The integration of reconfigurable intelligent surfaces (RISs) and unmanned aerial vehicles (UAVs) has emerged as a promising solution for enhancing connectivity in future wireless networks. This paper designs well-connected and resilient UAV networks by deploying and virtually partitioning multiple RISs to create multiple RIS-aided links, focusing on a link-layer perspective. The RIS-aided links are created to connect user equipment (UE) to blocked and reliable UAVs, where multiple UEs can transmit to same UAV via RIS using non-orthogonal multiple access (NOMA), granting access to UEs and maximizing network connectivity. We first derive exact and approximated closed-form expressions for signal-to-interference plus noise ratio (SINR) based on aligned and non-aligned RIS-aided beams. Then, we propose to formulate the problem of maximizing network connectivity that jointly considers (i) UE NOMA clustering, (ii) RIS-aided link selection, and (ii) virtual RIS partitioning. This problem is a computationally expensive combinatorial optimization. To tackle this problem, a two-step iterative approach, called RIS-aided NOMA, is proposed. In the first step, the UEs are clustered to the RISs according to their channel gains, while UAVs are associated to those generated clusters based on their reliability, which measures the criticality of UAVs. The second step optimally partitions the RISs to support each of the cluster members. In this step, we derive the closed-form equations for the optimal partitioning of RISs within the clusters. Simulation results demonstrate that the proposed RIS-aided NOMA yields a gain of 30% to 40%, respectively, compared to UAV traditional scheme. The finding emphasizes the potential of integrating RIS with UAV communications as a robust and reliable connectivity solution for future wireless communication systems.