  We study the effect of periodic hopping modulation on a Su-Schrieffer-Heeger
(SSH) chain that exhibits non-Hermiticity in presence of an onsite staggered
imaginary potential. This dissipative, non-Hermitian (NH) extension amply
modifies the features of the topological trivial phase (TTP) and the
topological nontrivial phase (TNP) of the SSH chain. Though a weak potential
can respect the parity-time ($\mathcal{PT}$) symmetry keeping the energy
eigenvalues real, a strong potential breaks $\mathcal{PT}$ conservation leading
to imaginary end state and complex bulk state energies in the system.
Furthermore for large commensurate periodicity of the hopping, in-gap states
appear that take either purely real or purely imaginary eigenvalues depending
on the strenth of both NH potential and hopping modulation. In particular, this
paper is engaged with hopping periodicities of 2, 4 and 8 lattice spacings. The
localization of end states and in-gap states at the boundaries are investigated
for those hopping periodicities. Though we find that topology and
$\mathcal{PT}$ symmetry are not very directly connected, distinguishing
distribution of $\mathcal{PT}$ broken and unbroken phases are clearly observed
within TNP and TTP in our systems.
