The escalating growth of the Internet of things (IoT) has intensified the demand for dependable and efficient communication networks to accommodate the massive data volumes produced by interconnected devices. Satellite networks have emerged as a promising alternative, particularly in remote and underserved regions where terrestrial communication infrastructures are inadequate. Nevertheless, guaranteeing secure uplink communications in satellite-based IoT networks is a daunting task due to similar satellite channels and limited resources at IoT nodes. In this paper, we explore the potential of unmanned aerial vehicle (UAV) to improve the secrecy performance of uplink transmissions in satellite-supported IoT networks. Specifically, we first introduce a framework for UAV-aided secure uplink communications, presuming a secure UAV-to-satellite connection. To mitigate the risks of ground eavesdroppers intercepting uplink transmissions, we develop a max-min secrecy rate optimization problem with uplink power constraints. To address this non-convex problem, a streamlined two-stage optimization approach is proposed. In inner stage, we combine uplink power allocation and UAV beamforming and propose a successive convex approximation (SCA) based joint optimization algorithm to address them. In outer stage, we propose an synergized bisection and coordinate descent algorithm to optimize UAV positioning. Convergence is attained by alternating iterations between these two stages. Particularly, the secrecy fairness among IoT users is reached by solving the max-min problem. Additionally, we offer a complexity analysis of the proposed algorithm and validate the efficacy of the presented approach through comprehensive simulation results.