<p>The integration of Low-Earth orbit (LEO) satellites and unmanned aerial vehicles (UAVs) is key to providing robust beyond-terrestrial connectivity. However, the coexistence of the two systems under shared-spectrum operation results in severe cross-tier interference and spectrum congestion. This paper presents a unified cognitive framework that synergizes reconfigurable intelligent surface (RIS)-assisted propagation control with underlay spectrum sharing in an integrated LEO–UAV OFDMA downlink. A UAV secondary transmitter opportunistically reuses the LEO satellite’s subcarriers while guaranteeing explicit SINR protection for primary satellite users. To mitigate interference and address heterogeneous propagation conditions, we jointly optimize the UAV’s three-dimensional placement, RIS phase configuration, per-subcarrier power allocation, and binary subcarrier assignment. The resulting mixed-integer non-convex optimization problem is solved using a penalty-and-projection framework instantiated with Particle Swarm Optimization (PSO) and Estimation of Distribution Algorithm (EDA). Extensive Monte-Carlo simulations demonstrate that the proposed joint design consistently outperforms LEO-only, UAV-only, and non-RIS baselines, achieving over 40% higher sum rate, up to 29% gains with RIS scaling, and up to 23% improvements under dense user deployments and UAV altitude variations. Crucially, the proposed framework reduces primary-tier outage probability by up to 75% under strict power budgets, offering a robust and scalable solution for spectral-efficient and reliable next-generation non-terrestrial networks. This reliable beyond-terrestrial connectivity enables IoT safety and autonomous exploration in remote mining operations, supporting Saudi Vision 2030.</p>