The synthesis of ternary core/shell zinc-blende CdTeSe/ZnSe quantum dots with optimal synthesis parameters is analyzed. For the synthesis of the ternary-alloy CdTeSe core, a temperature around 260 °C is shown to allow a good reaction of both the Te and Se reagents, while for lower temperatures mostly-CdTe quantum dots are synthesized. At this temperature, by changing the ratio of the Te and Se reagents, the composition can be tuned from Te-rich to Se-rich while keeping a constant quantum dot size. The photoluminescence wavelength expands up to 860 nm for the core CdTeSe and 900 nm for the CdTeSe/ZnSe samples, a near-infrared bandgap with potential applications in photovoltaics. The use of Raman spectroscopy is proved especially useful to analyze the composition of the alloy quantum dots, with the presence of two longitudinal-optical phonon lines corresponding respectively to CdTe and CdSe vibrations. For single core/shell CdTeSe/ZnSe quantum dots, perfect single-photon emission is demonstrated with good stability and low blinking, and a long decay time of 110 ns suggesting high luminescence quantum yield.