This paper investigates the performance of downlink non-orthogonal multiple access (NOMA) communication in unmanned aerial vehicle (UAV) networks enhanced by partitionable reconfigurable intelligent surfaces (RISs). We analyze three types of links between base station (BS) and UAVs: direct, RIS-only indirect, and composite links, under both Line-of-Sight (LoS) and Non-LoS (NLoS) propagation. The RIS-only indirect link and direct link are modeled using double Nakagami-m and Nakagami-m fading, respectively, while the composite link follows a combined fading channel model. Closed-form expressions for the cumulative distribution function (CDF) of the received signal-to-noise ratio (SNR) are derived for all links, enabling tractable outage probability analysis. Then, we formulate a fairness-efficiency bilevel optimization problem to minimize the maximum outage probability among UAVs while minimizing the total number of required RIS reflecting elements. Accordingly, an RIS-assisted UAV Outage Minimization (RUOM) algorithm is proposed, which fairly allocates the NOMA power coefficients while minimizing the total number of RIS reflecting elements required, subject to NOMA-defined constraints, RIS resource limitations, and maximum allowable outage threshold. Simulation results validate the analytical models and demonstrate that the proposed RUOM algorithm significantly improves fairness and efficiency in BS-UAV communication.