This paper is concerned with the ultimate boundedness control problem for a class of networked nonlinear systems subject to the try-once-discard (TOD) protocol scheduling and uniform quantization effects. To prevent the transmission data from collisions, the communication between sensor nodes and the controller is implemented via a constrained communication channel, where only one sensor node is permitted to transmit data at each time instant. The TOD protocol is utilized to regulate the signal transmission over the communication network under which the scheduling behavior is described by a special switching function. On the other hand, the uniform quantization effects of the network are characterized by a round function (i.e., the nearest integer function). The purpose of the addressed problem is to design an observer-based controller for the networked nonlinear systems such that, in the presence of TOD protocol and uniform quantization effects, the closed-loop system is ultimately bounded and the controlled output is locally minimized. Sufficient conditions are established to guarantee the ultimate boundedness of the dynamics of the closed-loop system in mean square by applying the stochastic analysis approach. Furthermore, the desired controller gains are derived by solving a convex optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design scheme.