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The Ly$α$ forest decomposed into Voigt profile components allow us to study clustering properties of the intergalactic medium and its dependence on various physical quantities. Here, we report the first detections of probability excess of low-z (i.e z<0.48) Ly$α$ absorber triplets over a scale of $r_\parallel\leq8$pMpc with a maximum amplitude of $8.76^{+1.96}_{-1.65}$ at a longitudinal separation of 1-2pMpc. We measure non-zero three-point correlation ($ζ=4.76^{+1.98}_{-1.67}$) only at this scale with reduced three-point correlation value of Q=$0.95^{+0.39}_{-0.38}$. The measured $ζ$ shows an increasing trend with increasing HI column density ($N_{HI}$) while Q does not show any $N_{HI}$ dependence. About 88% of the triplets contributing to $ζ$ (at z$\le0.2$) have nearby galaxies (whose distribution is known to be complete for 0.1L$_*$ at z<0.1 and for L$_*$ at z~0.25 and within 20' to the quasar sightlines) within a velocity separation of 500$kms^{-1}$ and a median impact parameter of 405pkpc. The measured impact parameters are consistent with appreciable number of triplets at z$\le0.2$ not originating from individual galaxies but tracing the underlying galaxy distribution. Frequency of occurrence of high-b absorbers in triplets (~85%) is a factor~3 higher than that found among the full sample (~32%). Using four different cosmological simulations, we quantify the effect of peculiar velocities, feedback effects and show that most of the observed trends are broadly reproduced. However, $ζ$ at small scales ($r_\parallel<1$pMpc) and b-dependence of $ζ$ in simulations are found inconsistent with the observations. This could either be related to the fact that none of these simulations reproduce the observed b-distribution and $N_{HI}$ distribution for $N_{HI}>10^{14}$cm$^{-2}$ self-consistently or to the widespread of signal-to-noise ratio in the observed data.