The high throughput demand from mobile subscribers can be satisfied by utilizing small cell aided ultra dense networks (UDNs). However, excessive deployment of such cells in UDNs results in significant increase in energy consumption of the network. This profusion in the consumption of energy can be handled by appropriately switching off some of the small cells during low data demand. This base station sleeping (BSS) cannot be performed alone as it has been shown that that the BSS adversely affects the network's coverage and throughput. To compensate for the loss in throughput due to BSS, we utilize non-orthogonal multiple access (NOMA) in this paper. The main objective of introducing NOMA along with BSS is to serve the users under the switched-off base station by pairing them as NOMA users within nearby base stations. Hence, we formulate the resource allocation in the downlink as an optimization problem for NOMA and BSS. We solve this problem for a given NOMA pairing and BSS. Through numerical results, we show that the NOMA combined with BSS results in improved network throughput and energy efficiency as compared to the benchmark system at the cost of reduced network coverage. © 2020 IEEE.