[en] We study the formation and detection at the next linear e⁺e^- collider of bound states of level-1 quark Kaluza-Klein excitations B_KK within a scenario of universal extra dimensions. The interactions of such Kaluza-Klein excitations are modeled by an α_s driven Coulomb potential. In order to obtain the threshold cross section, we employ the Green function method which is known to properly describe the peaks below threshold and to yield a net increase in the continuum region (above threshold) relative to the naive Born cross section. We study such effect at different values of the scale (R^-1) of the extra dimensions with an explicit calculation for the mass spectrum as given by radiative corrections. The overall effect is roughly 2.7 at R^-1=300 GeV and goes down to 2.2 at R^-1=1000 GeV and a relatively large number of events is expected from N_events≅2.5x10⁴ at R^-1=300 GeV down to N_events≅10³ at R^-1=1000 GeV at the anticipated annual integrated luminosity of L₀=100 fb^-1. We finally discuss some potentially observable signatures such as the multilepton channels 2j+2l+Ee and 2j+4l+Ee for which we estimate statistical significance > or approx. 2 for R^-1 up to 600∼700 GeV.