  In the context of a gauge invariant, non-anomalous and family-dependent
(non-universal) $U(1)'$ extension of the Standard Model, wherein a new high
scale mechanism generates masses and couplings for the first two fermion
generations and the standard Higgs mechanism does so for the third one, we find
solutions to the anomaly observed by the Atomki collaboration in the decay of
excited states of Beryllium, in the form of a very light $Z'$ state, stemming
from the $U(1)'$ symmetry breaking, with significant axial couplings so as to
evade a variety of low scale experimental constraints.
