  Ultralight primordial black holes (PBHs)($\lesssim10^9$g) completely
evaporate via Hawking radiation (HR) and produce all the particles in a given
theory regardless of their other interactions. If the right handed (RH)
neutrinos are produced from PBH evaporation, successful baryogenesis via
leptogenesis predicts mass scale of RH neutrinos as well as black holes. We
show that, given the lepton number violation (generation of RH neutrino masses)
in the theory is a consequence of a gauged $U(1)$ breaking which is then
followed by the formation of PBHs, a network of cosmic strings naturally gives
rise to strong stochastic gravitational wave (GW) signal at the sensitivity
level of pulsar timing arrays (PTA) and LIGO5. Besides, due to a transient
period of black hole domination in the early universe, for which baryon
asymmetry is independent of initial PBH density, a break in the GW spectra
occurs around MHz frequency. Therefore, to observe the break along with the
usual GW signal by the emission of gravitons via HR, GW detectors at higher
frequencies are called for. The recent finding by the NANOGrav PTA of a
stochastic common spectrum process (interpreted as GWs) across many pulsars is
in tension with PBH baryogenesis for large cosmic string loops ($\alpha\simeq
0.1$).
