Heavy-metal-free indium phosphide (InP)-based quantum dots (QDs) have attracted much attention as materials for display applications. Methods such as introducing Zn in the core of InP QDs and passivating wide band-gap materials have been used to improve the luminescent properties of InP QDs. Herein, we investigated the photophysical properties of the In(Zn)P core QDs with the influence of the Zn additive on the InP QDs. The near band edge photoluminescence (PL) of the In(Zn)P QDs was spectrally asymmetric in shape, with a redshifted side peak originating from a Zn impurity that induced shallow defect sites, resulting in PL linewidth broadening. The shallow trap emission of the In(Zn)P QDs disappeared after the overcoating of the ZnSeS passivated the shell layers, and the PL linewidth of In(Zn)P/ZnSeS (core/shell) QDs was solely determined by the band-edge excitonic energy distribution caused by the size dispersion in ensemble QD systems. We expect that the understanding the photophysical properties of In(Zn)P-based QDs future strategies to narrow the ensemble emission line of the InP-based QD synthesis.