  In this paper we study two newly discovered classes of radio sources: the
highly energetic, short-lived events, known as Fast Radio Bursts (FRBs), and a
new category of compact sources known as Fanaroff-Riley type 0 radio galaxies
(FR0s). Due to a possible catastrophic event origin for the FRBs and a previous
correlation found with an FR0 in the gamma ray spectrum, it is possible that
these radio sources could also emit high energy photons in the Fermi-LAT
satellite energy range (20 MeV - 300GeV). Here we present an exhaustive
time-dependent and spatial search of all up-to-date observed FRBs and FR0s,
respectively. We perform a likelihood analysis of the radio sources by modeling
the excess flux of gamma rays with a varying index power law function using
data from Fermi-LAT and the 4FGL catalog. Sources with test statistic greater
than 16 (corresponding to about 4{\sigma}) were further analyzed including 2
FRBs and 7 FR0s. No correlations with more than 5{\sigma} were found after
taking into account nearby sources. Therefore, upper limits for all sources
were calculated
