gradually attracted extensive interest in academia and industry [1,2]. Supporting massive connections and a low latency are two of the main distinguishing features of 6G networks. Millimeter waves and NOMA are two important techniques that can significantly improve spectral efficiency. Millimeter wave technology can achieve high speeds and reliability by enhancing various wireless links in 5G communication, and can be used as terahertz in 6G communication [3,4]. NOMA is capable of sharing the same bandwidth resources among multiple users [5,6]. As one of the important schemes of NOMA, Sparse Code Division Multiple Access (SCMA) combines code domain signal superposition, a sparse spread spectrum, and multi-dimensional constellation design, so that the SCMA system has a high overload gain and a high frequency spectral efficiency while maintaining low complexity [7]. Successive interference cancellation (SIC) is implemented at nearby users with a stronger channel to strike out the interference from distant users. An exceptional spectral efficiency of NOMA has been attained by invoking users' distinguishing channel conditions or a quality of service (QoS) [8]. Low-latency communications are the foundation for enabling business-sensitive applications with rigorous QoS [9,10]. A short packet with finite blocklength codes is an efficient approach to achieve low-latency communications, where the effective capacity can be employed to characterize the performance of wireless networks under the condition of certain delay constraints [11]. Due to the finitude of blocklength, the decoding error probability of a receiver cannot be ignored in short packet communications. As a result, it is pivotal to highlight the performance of NOMA networks with low-latency communications [12, 13, 14]. The authors of [12] studied the trade-off between transmission latency and decoding error probability. In [13], the closed-form expressions of block error rates (BERs) were derived, and the superior performance of NOMA was proved by reducing transmission delay. Through the optimization of the transmission rate and power allocation, the authors of [14] aimed to maximize the effective throughput of users with a high channel gain and ensure that other users meet the lowest effective throughput for short-packet communications. In [15], the authors introduced NOMA technology to secure short packet communication in the IoT. In [16], the effects of the transmission signal-to-noise ratio (SNR) and the delay exponent on the effective capacity and queue delay violation probability were studied for low-latency communications. The author in [17] optimized the resources of the multi-carrier NOMA system for packet communication. Through joint carrier allocation and transmission power allocation, the transmission rate is allocated to each user to maximize the total weighted effective throughput. The authors in [18,19] researched the capacity of NOMA networks, but the performance of the last user was not taken into consideration. To the best of our knowledge, the effective capacities of \(M\) users for NOMA networks with finite blocklength have not been well addressed. In light of the above discussions, we studied the NOMA latency performance with a finite blocklength. New closed-form and asymptotic expressions of effective capacity for sorted users were derived using Gauss-Laguerre quadrature. Numerical simulation shows that (1), as the blocklength decreases, non-orthogonal users are capable of attaining a larger effective capacity, and (2) the diversification of the error probability and the delay exponent has a great impact on users' effective capacities. The rest of this paper is organised as follows. Section 2 describes the model of the NOMA system with short packet communications. In Section 3, we derived both new exact and asymptotic expressions of effective capacities and then obtained high SNR slopes of effective capacity in NOMA networks.