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This paper investigates the impact of authentication on effective capacity (EC) of an underwater acoustic (UWA) channel. Specifically, the UWA channel is under impersonation attack by a malicious node (Eve) present in the close vicinity of the legitimate node pair (Alice and Bob); Eve tries to inject its malicious data into the system by making Bob believe that she is indeed Alice. To thwart the impersonation attack by Eve, Bob utilizes the distance of the transmit node as the feature/fingerprint to carry out feature-based authentication at the physical layer. Due to authentication at Bob, due to lack of channel knowledge at the transmit node (Alice or Eve), and due to the threshold-based decoding error model, the relevant dynamics of the considered system could be modelled by a Markov chain (MC). Thus, we compute the state-transition probabilities of the MC, and the moment generating function for the service process corresponding to each state. This enables us to derive a closed-form expression of the EC in terms of authentication parameters. Furthermore, we compute the optimal transmission rate (at Alice) through gradient-descent (GD) technique and artificial neural network (ANN) method. Simulation results show that the EC decreases under severe authentication constraints (i.e., more false alarms and more transmissions by Eve). Simulation results also reveal that the (optimal transmission rate) performance of the ANN technique is quite close to that of the GD method.