The ANtarctic Impulsive Transient Antenna (ANITA) long-duration balloon experiment is sensitive to interactions of ultrahigh-energy (E>1018 eV) neutrinos in the Antarctic ice sheet. The third flight of ANITA, lasting 22 days, began in December 2014. We develop a methodology to search for energetic neutrinos spatially and temporally coincident with potential source classes in ANITA data. This methodology is applied to several source classes: the potential IceCube-identified neutrino sources TXS 0506+056 and NGC 1068, flaring high-energy blazars reported by the Fermi All-Sky Variability Analysis, gamma-ray bursts, and supernovae. Among searches within the five source classes, one candidate was identified as associated with SN 2015D, although not at a statistically significant level. We proceed to place upper limits on the source classes. We further comment on potential application of this methodology to more sensitive future instruments
