  The ANtarctic Impulsive Transient Antenna (ANITA) long-duration balloon
experiment is sensitive to interactions of ultra high-energy (E > 10^{18} 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 TXS
0506+056 blazar and NGC 1068, the first potential TeV neutrino sources
identified by IceCube, 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
applications of this methodology to more sensitive future instruments.
