  The multiple parton$-$parton interactions (MPIs) are an important element to
describe the observed collective flow and strangeness enhancement in high
multiplicity pp and p$-$Pb collisions, the so-called small systems. At LHC
energy, MPIs affect both soft and hard scales of the event. Since quarkonium
production involves both, it can be an excellent tool to understand the role of
MPIs in small systems. Study of multiplicity dependent quarkonium production
provides an indirect probe of MPIs in hadronic collisions. Also, relative
production of excited-to-ground quarkonium states as a function of multiplicity
are sensitive to final state effects. Cross section measurements of different
quarkonium states are also important to understand their production mechanisms.
In these proceedings, first preliminary results of $\psi$(2S)-over-J/$\psi$
cross section measurements at mid and forward rapidity ($\textit{y}$) from Run
2 and Run 3 pp collisions at $\sqrt{s}$ = 13 and 13.6 TeV, respectively will be
presented. Preliminary results on $\Upsilon$(nS) states (n = 1,2) cross
sections and final multiplicity dependent measurements of excited-to-ground
states quarkonium yields, at forward $\textit{y}$, in pp collisions at
$\sqrt{s} =$ 13 TeV will be shown. In addition, few performance plots from Run
3 in the quarkonium sector will be presented and discussed.
