  In this work, we assess the sensitivity reach of pulsar timing array (PTA)
measurements to probe pointlike primordial black holes (PBHs), with an extended
mass distribution, which originate from collapsed Fermi balls that are formed
through the aggregation of asymmetric U(1) dark fermions trapped within false
vacuum bubbles during a dark first order phase transition (FOPT). The PBH
formation scenario is mainly characterized by the dark asymmetry, strength of
the FOPT, rate of FOPT, and the percolation temperature. Meanwhile, for PBH
masses of interest lying within $10^{-10} M_\odot - 10^{2}M_\odot$, the
relevant signal for PTA measurements is the Doppler phase shift in the timing
signal, due to the velocity change induced by transiting PBHs on pulsars.
Taking the dark asymmetry parameter to be $10^{-4}$ and $10^{-5}$, we find that
percolation temperatures within the 0.1-10 keV range, FOPT rates above $10^3$
times the Hubble parameter at percolation, and FOPT strengths within
$10^{-6}-0.1$ can give rise to PBHs that can be probed by an SKA-like PTA
observation. On the other hand, the accompanying gravitational wave (GW) signal
from the FOPT can be used as a complementary probe, assuming that the peak
frequency lies within the $\mathcal{O}(10^{-10})-\mathcal{O}(10^{-7})$ Hz
range, and the peak GW abundance is above the peak-integrated sensitivity
curves associated with pulsar timing observations that search for stochastic
GWs. At the fundamental level, a quartic effective potential for a dark scalar
field can trigger the FOPT. By performing a parameter scan, we obtained the
class of effective potentials that lead to FOPT scenarios that can be probed by
SKA through pulsar timing and GW observations.
