Lepton Flavour Violation (LFV) is one of the important topics of High-Energy Physics in recent days
and $\Upsilon$ is one of the suited candidates to explore the early universe. Upsilons decay into muons through the annihilation of the bound state of quarks and gluons. Since the discovery of these particles,
they have drawn much attention in understanding their characteristics experimentally and theoretically. The radiative and the lepton flavour-conserving decays are already well established via observations in small systems. On the other hand, their lepton flavour violating part is still unexplored in colliders and also in BSM physics. Also, this quarkonium candidate shows
unique behaviour at high temperatures and densities. The colliders are also probing the LFV decays in the search of NP. Motivated by the study of the LFV decays, we will present and discuss various LFV decays of Upsilons, incorporating the contribution of the Z' boson. Here, we have also constrained the maximum allowed values of the New Physics (NP) quark couplings to predict the upper
bound of the LFV branching ratios. The NP couplings are constrained with the available experimental data using the chi-square fitting technique. Connections of BSM physics with QCD avenues will be also presented and discussed.