  We investigate the production of fermionic dark matter $\chi$ via $pp \to
p\gamma p \to p j \chi \bar{\chi}X$ mediated by a leptophobic spin-1 particle,
where one of the protons remains intact and is tagged by forward proton
detectors. We find that the masses of $\chi$ and the mediator $Z'$ are severely
constrained when $Z'$ interacts with $\chi$ and quarks through the vector
couplings. We show that dark matter searches in this production channel are
sensitive to a mediator mass $m_{Z'} \lesssim 1.4~\mathrm{TeV}$ at 14 TeV at
the LHC with an integrated luminosity $L_{\rm{int}} = 3000~\rm{fb}^{-1}$. The
lower mass bound on the dark matter is $m_\chi \simeq 550~\mathrm{GeV}$ at the
mediator mass $m_{Z'}=1.2~\mathrm{TeV}$.
