  We extend the analysis of \cite{Chowdhury:2019hns} to study the Regge
trajectories of the Mellin amplitudes of the $0-$ and $1-$ magnon correlators
of the generalized Fishnet theory in $d$ dimensions and one type of correlators
of chiral fishnet theory in $4$ dimensions. We develop a systematic procedure
to perturbatively study the Regge trajectories and subsequently perform the
spectral integral. Our perturbative method is very generic and in principle can
be applied to correlators whose perturbative Regge trajectories obey some
structural conditions which we list down. Our $d$ dimensional results reduce to
previously known results in $d=4$ for 0-magnon and 1- magnon. As a non trivial
check, we show that the results for 1-magnon correlator in $d=8$, when
evaluated using the exact techniques in \cite{Chowdhury:2019hns,
Korchemsky:2018hnb} are in perfect agreement with our $d$ dimensional
perturbative results. We also perturbatively compute the Regge trajectories and
Regge-Mellin amplitudes of the chiral fishnet correlator $\langle{\rm
Tr}[\phi_1(x_1)\phi_1(x_2)]{\rm
Tr}[\phi_1^\dagger(x_3)\phi_1^\dagger(x_4)]\rangle$ using the techniques
developed in this paper. Since this correlator has two couplings $\kappa$ and
$\omega$, we have obtained closed-form results in the limit $\kappa \to 0,
\omega \to 0$ with $\kappa/\omega$ held constant. We verify this computation
with an independent method of computing the same and obtain perfect agreement.
