In this paper, we develop a theoretical framework for analyzing the transmission outage probabilities of adaptive reconfigurable intelligent surfaces (RISs)-assisted non-orthogonal multiple access (NOMA) systems over Fisher-Snedecor F fading channels. Taking into consideration a quality of service (QoS)-sensitive users and non-sensitive QoS users, but requiring secure transmissions, we study an adaptive transmission of non-sensitive QoS users by proposing an adaptive channel model subject to conditions of sensitive QoS users, combined with non-orthogonal multiple access (NOMA) to negotiate with the secure transmission of non-sensitive QoS. Under settings of coherent and discrete phase-shift models adopted at the RIS and imperfect successive interference cancellation, we derive the outage probability (OP) and ergodic capacity (EC) for both fixed and adaptive power allocation (PA) criteria for channel adaptation models and adaptive PA criteria for non-channel adaptation models in closed-form expressions. Then, we further carry out an asymptotic outage analysis to achieve insightful findings into system designs, specifically the diversity order that the system achieves. Finally, we present several numerical results based on Monte Carlo simulations to validate our developed mathematical frameworks.