Aims: To unveil the influence of galaxy-galaxy interactions on material transport driven by galactic bars towards the central regions of active galactic nuclei (AGN) galaxies and assess the efficiency of the combined mechanisms of interactions and bars in fueling massive black holes, we examine barred active galaxies in paired systems. Methods: Our study targets barred AGN galaxies in pairs with projected separations $r_{p}< 100 \rm \,kpc \,h^{-1}$ and relative radial velocities of $\Delta V< 500 \rm \,km \,s^{-1}$ within $z<0.1$, using Sloan Digital Sky Survey (SDSS) data. To quantify the impact of interactions, we also created a control sample of barred active galaxies without companions, matched in redshift, absolute r-band magnitude, stellar mass, color, and stellar age. We assessed galactic bar structures through two-dimensional image modeling, considering their wide range of shapes and sizes that may affect material transport ability. Results: We found that nuclear activity, measured by $Lum[OIII]$, increases as projected separations between galaxy pair members decrease. Barred AGN galaxies in close pairs ($r_p<$ 25 kpc $h^{-1}$) show significantly higher nuclear activity compared to the control sample. Barred galaxies with close companions exhibit enhanced nuclear activity across all luminosity, stellar mass, and color ranges. Barred AGN with longer bars show more efficient nuclear activity than those with shorter bars, with a pronounced effect in close pair systems. Nuclear activity increases as pair separations decrease. Barred AGNs in close pairs undergoing major interactions show a substantial excess of high $Lum[OIII]$ values, reflecting increased accretion onto central black holes. These findings suggest that nearby galaxy companions enhance gas flows driven by galactic bars, amplifying central nuclear activity and influencing black hole accretion.