We present a physical investigation on the generation of correlated photon pairs that are broadly spaced in the ultraviolet (UV) and visible spectrum on a AlGaN/AlN integrated photonic platform which is optically transparent at these wavelengths. Using spontaneous four wave mixing (SFWM) in an AlGaN microring resonator, we show design techniques to satisfy the phase matching condition between the optical pump, the signal, and idler photon pairs, a condition which is essential and is a key hurdle when operating at short wavelength due to the strong normal dispersion of the material. Such UV-visible photon pairs are quite beneficial for interaction with qubit ions that are mostly in this wavelength range, and will enable heralding the photon-ion interaction. As a target application example, we present the systematic AlGaN microresonator design for generating signal and idler photon pairs using a blue wavelength pump, while the signal appears at the transition of ytterbium ion (171Yb+, 369.5 nm) and the idler appears in the far blue or green range. The photon pairs have minimal crosstalk to the pump power due to their broad spacing in spectral wavelength, thereby relaxing the design of on-chip integrated filters for separating pump, signal and idler.