Quantum dots (QDs) formed in semiconductor nanowires (NWs) form a basis for studying interesting quantum phenomena and provide an exciting platform for various device applications, where in-depth understanding of the formation and electronic properties of such QDs is a requirement. In this work we present detailed investigations of structural, electronic, and optical properties of nitrogen-induced self-assembled QDs in novel Ga(N,As,P) NWs. We show that the three-dimensional quantum confinement of the excitons caused by short-range fluctuations in the N content leads to single-photon emission. We demonstrate that valence band character varies between the QD emitters and attribute it to a varying degree of hole localization within the QDs induced by fluctuations in the As/P ratio. These fluctuations in the chemical compositions are also believed to be at least partly responsible for the observed large variation in exciton lifetimes of the QDs, ranging between 0.5 and 10 ns. The rather long lifetimes demonstrate the resilience of the QDs to nonradiative recombination-a merit for efficient single-photon emitters. Furthermore, we show that the principal axes of the formed QDs are oriented radially, normal to the NW side facets, in contrast to the N-induced QDs in GaNAs NWs which are primarily aligned along the NW axis. Our results, therefore, underline the impacts of the host alloy on the QD formation, which could provide an additional degree of freedom for band structure engineering in nanowires.