Probing the minimal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>X</mml:mi></mml:msub></mml:math> model at future electron-positron colliders via fermion pair-production channels

The minimal $U(1{)}_{X}$ extension of the Standard Model (SM) is a well-motivated new physics scenario, where anomaly cancellation dictates neutral gauge boson (${Z}^{\ensuremath{'}}$) couplings with SM fermions in terms charges scalar fields. We investigate charged fermion pair-production process for different values these at future ${e}^{\ensuremath{-}}{e}^{+}$ colliders: ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}f\overline{f}$. Apart from standard $\ensuremath{\gamma}$ and $Z$-mediated processes, this model features additional $s$-channel (or both $s$ $t$-channel when $f={e}^{\ensuremath{-}}$) ${Z}^{\ensuremath{'}}$ exchange which interferes processes. first estimate bounds on coupling $({g}^{\ensuremath{'}})$ mass $({M}_{{Z}^{\ensuremath{'}}})$ considering latest dilepton dijet constraints heavy resonance searches LHC. Then using allowed ${g}^{\ensuremath{'}}$, we study angular distributions, forward-backward $({\mathcal{A}}_{\mathrm{FB}})$, left-right $({\mathcal{A}}_{\mathrm{LR}})$, $({\mathcal{A}}_{\mathrm{LR},\mathrm{FB}})$ asymmetries $f\overline{f}$ final states. find that observables can show substantial deviations results model, thus providing powerful probe multi-TeV bosons ${e}^{+}{e}^{\ensuremath{-}}$ colliders.