Nitride cylindrical quantum dots (NCQDs) are commonly used materials in optical chemical sensors and biosensors. We investigated the exciton-related optical properties of wurtzite ZnSnN2/InxGa1−xN cylindrical quantum dots (CQDs) with finite potential barriers. The energy states in a CQD system were computed by a variational scheme using the single-band effective mass approximation, which considers the effect of the built-in electric field (BEF). The results are presented in the form of a specific function of CQD structural parameters including height, radius, and In concentration in the barrier. Our major findings are as follows. First, the excitonic transition energy decreases with increasing CQD size and increases with increasing In concentration. Second, the oscillator strength rapidly decreases with increasing CQD height and slowly increases with increasing CQD radius. Furthermore, we obtained the absorption coefficient (AC) of the exciton as a function of the incident photon energy for different CQD structural parameters. We concluded that, in general, increasing any of the aforementioned structural parameters causes either a blueshift or redshift of the AC peak. A similar phenomenon occurs for the resonant peak intensity. In particular, a strong BEF leads to a redshift of the resonant peak and a decrease in its intensity.