This paper studies an Internet-of-Things (IoT) network employing a reconfigurable intelligent surface (RIS) over generalized fading channels. Inspired by the promising potential of RIS-based transmission, we investigate a RIS-enabled IoT network with the source node employing a RIS-based access point. The system is modelled with reference to a receiver transmitter pair and the Fisher-Snedecor F model is adopted to analyse the composite fading and shadowing channel. Closed-form expressions are derived for the system with regards to the average capacity, average bit error rate (BER) and outage probability. Monte-Carlo simulations are provided throughout to validate the results. The results investigated and reported in this study extend early results reported in the emerging literature on RIS-enabled technologies and provides a framework for the evaluation of a basic RIS-enabled IoT network over the most common multipath fading channels. The results indicate the clear benefit of employing a RIS-enabled access point, as well as the versatility of the derived expressions in analysing the effects of fading and shadowing on the network. The results further demonstrate that for a RIS-enabled IoT network, there is the need to balance between the cost and benefit of increasing the RIS cells against other parameters such as increasing transmit power, especially at low SNR and/or high to moderate fading/shadowing severity.