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The research of Non-Orthogonal Multiple Access (NOMA) is extensively used to improve the capacity of networks beyond the fifth-generation. The recent merger of NOMA with ambient Backscatter Communication (BackCom), though opening new possibilities for massive connectivity, poses several challenges in dense wireless networks. One such challenge is the performance degradation of ambient BackCom in multi-cell NOMA networks under the effect of inter-cell interference. Driven by providing an efficient solution to the issue, this article proposes a new resource allocation framework that uses a duality theory approach. Specifically, the sum rate of the multi-cell network with backscatter tags and NOMA user equipment is maximized by formulating a joint optimization problem. To find the efficient base station transmit power and backscatter reflection coefficient in each cell, the original problem is first divided into two subproblems, and then the closed form solution is derived. A comparison with the Orthogonal Multiple Access (OMA) ambient BackCom and pure NOMA transmission has been provided. Simulation results of the proposed NOMA ambient BackCom indicate a significant improvement over the OMA ambient BackCom and pure NOMA in terms of sum-rate gains.