We investigated the effect of ternary shell alloy composition on the binary core bandgap and diameter of CdSe/Cd1-xZnxS heterostructure core/shell nanocrystals synthesized by a simple colloidal technique. The structural properties were characterized by using the x-ray diffraction (XRD) and the transmission electron microscopy (TEM) techniques, whereas the optical absorption and emission properties were characterized by using the UV-Vis and Photoluminescence spectrometers, respectively. We determined the bandgap of CdSe core capped with Cd1-xZnxS ternary alloy shell from the optical absorption spectra, which shows a parabolic dependence of core band gap on the ternary shell alloy composition as E-g(ne) (x)= 2.11.0.08x+ 0.32x(2) in the strong confinement regime. Furthermore, the core diameter 3.80 nm determined from the TEM measurement after capping CdSe core with Cd1-xZnxS ternary shell layer is in good agreement with the calculated values based on two parabolic band effective mass approximation with the interface strain and composition effects considered. The results suggests that the core diameter and band gap of binary/ternary core/shell quantum dots can be modified with interface strain and alloy composition. As dimension of semiconductor devices reduce towards nanoscale to increase the device speed and performance, such findings can give the device scientists and engineers an extra degree of freedom in the design of core/shell quantum dots for their tunable optoelectronic properties.