  In this work we perform an exploratory study of the photoproduction of
singlet QED bound states $(l^-l^+)_S$ in electron - ion collisions at the EicC,
EIC and LHeC energies. The total cross - sections, event rates per year and
rapidity distributions associated with the parapositronium, paramuonium and
paratauonium production are estimated. Moreover, we consider the decay of these
states in a two - photon system and implement kinematical cuts on the
rapidities and energies of the photons in the final state. We demonstrate the
paramuonium can, in principle, be observed for the first time in all these
colliders and that the EIC is a potential collider to discover the paratauonium
state.
