  Exclusive heavy quarkonium photoproduction is one of the most popular
processes in EIC, which has a large cross section and a simple final state. Due
to the gluonic nature of the exchange Pomeron, this process can be related to
the gluon distributions in the nucleus. The momentum transfer dependence of
this process is sensitive to the interaction sites, which provides a powerful
tool to probe the spatial distribution of gluons in the nucleus. Recently the
problem of the origin of hadron mass has received lots of attention in
determining the anomaly contribution $M_{a}$. The trace anomaly is sensitive to
the gluon condensate, and exclusive production of quarkonia such as J/$\psi$
and $\Upsilon$ can serve as a sensitive probe to constrain it. In this paper,
we present the performance of the ECCE detector for exclusive J/$\psi$
detection and the capability of this process to investigate the above physics
opportunities with ECCE.
