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The combination of backscatter communication with non-orthogonal multiple access (NOMA) has the potential to support low-powered massive connections in upcoming sixth-generation (6G) wireless networks. More specifically, backscatter communication can harvest and use the existing RF signals in the atmosphere for communication, while NOMA provides communication to multiple wireless devices over the same frequency and time resources. This paper has proposed a new resource management framework for backscatter-aided cooperative NOMA communication in upcoming 6G networks. In particular, the proposed work has simultaneously optimized the base station's transmit power, relaying node, the reflection coefficient of the backscatter tag, and time allocation under imperfect successive interference cancellation to maximize the sum rate of the system. To obtain an efficient solution for the resource management framework, we have proposed a combination of the bisection method and dual theory, where the sub-gradient method is adopted to optimize the Lagrangian multipliers. Numerical results have shown that the proposed solution provides excellent performance. When the performance of the proposed technique is compared to a brute-forcing search technique that guarantees optimal solution however, is very time-consuming, it was seen that the gap in performance is actually 0\%. Hence, the proposed framework has provided performance equal to a cumbersome brute-force search technique while offering much less complexity. The works in the literature on cooperative NOMA considered equal time distribution for cooperation and direct communication. Our results showed that optimizing the time-division can increase the performance by more than 110\% for high transmission powers.