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The rapidity dependent transverse momentum spectra of heavy quarkonia (J/ψ and Υ mesons) produced in small collision systems such as proton-proton (pp) and proton-lead (p-Pb) collisions at center-of-mass energy (per nucleon pair) s (sNN) = 5-13 TeV are described by a two-component statistical model which is based on the Tsallis statistics and inverse power-law. The experimental data measured by the LHCb Collaboration at the Large Hadron Collider (LHC) are well fitted by the model results. The related parameters are obtained and the dependence of parameters on rapidity is analyzed.