  We study and compare various $Z'$ models arising from $SO(10)$, focussing in
particular on the Abelian subgroup $U(1)_{R} \times U(1)_{B-L}$, broken at the
TeV scale to Standard Model hypercharge $U(1)_{Y}$. The gauge group $U(1)_{R}
\times U(1)_{B-L}$, which is equivalent to the $U(1)_{Y}\times U(1)_{\chi}$ in
a different basis, is well motivated from $SO(10)$ breaking and allows neutrino
mass via the linear seesaw mechanism. Assuming supersymmetry, we consider
single step gauge unification to predict the gauge couplings, then consider the
detection and characterisation prospects of the resulting $Z'$ at the LHC by
studying its possible decay modes into di-leptons as well as into Higgs bosons.
The main new result here is to analyse in detail the expected leptonic
forward-backward asymmetry at the high luminosity LHC and show that it may be
used to discriminate the $U(1)_{R} \times U(1)_{B-L}$ model from the usual
$B-L$ model based on $U(1)_{Y}\times U(1)_{B-L}$.
