We study the production sensitivity of Higgs bosons $h$ and $H$, in relation to the possible existence of $Z^{\prime }$ boson and a top quark pair at the energy scales that will be reached in the near future at projected $e^{+}{e}^{-}$ linear colliders. We focus on the resonance and no-resonance effects of the annihilation processes $e^{+}{e}^{-}\to (\gamma ,Z,Z^{\prime })\to t\stackrel{-}{t}h$ and $e^{+}{e}^{-}\to (\gamma ,Z,Z^{\prime })\to t\stackrel{-}{t}H$. Furthermore, we develop and present novel analytical formulas to assess the total cross section involved in the production of Higgs bosons. We find that the possibility of performing precision measurements for the Higgs bosons $h$ and $H$ and for the $Z^{\prime }$ boson is very promising at future $e^{+}{e}^{-}$ linear colliders.