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