The research delves into the intricate domain of security offloading within the context of non-orthogonal multiple access (NOMA) heterogeneous mobile edge computing (het-MEC) networks operating over Rayleigh fading channels. The investigation centers on a system model comprising a single antenna-equipped edge user, denoted as U, which strategically offloads computational tasks to two distinct heterogeneous wireless access points (APs): the far AP (AP1) and the near one (AP2), employing NOMA techniques. Notably, the research accounts for a passive eavesdropper (E) intending to intercept the U−AP2 transmission. A four-phase protocol is proposed to ensure the security offloading process, namely SAPS, which leverages wireless access point selection (APS) and physical layer security (PLS) techniques. The focus extends to derive a closed-form expression for a novel critical system performance metric: the secrecy successful computation probability (SSCP). Furthermore, an algorithm based on Ant Colony Optimization (ACO) within the continuous domain is introduced, which aims to enhance the SSCP by intelligently determining system parameters. The impact of critical factors such as transmit power, power allocation coefficient, bandwidth, CPU frequency, and task division ratio under the SAPS scheme is explored and compared to the conventional approach using pure NOMA. Remarkably, the algorithm in the proposed scheme demonstrates up to a 3% performance improvement. The validity and accuracy of the study findings are verified through Monte-Carlo simulations. The work contributes significantly to advancing secure offloading strategies in NOMA-based MEC networks, offering valuable insights for practical deployment and optimization.