Use the axes ButtonDown callback function (added to app designer in R2020b). Rt click on the UIAxes and select 'Callbacks > add UIAxesButtonDown callback function'.
Whatever code you want to execute when you left click on the image goes in this callback function.
There is some setup to get this to work with an image. Namely, you need to set the image object HitTest property to 'off'. There are a number of ways to do this. The default UIAxes callback execution control properties should be set correctly already (worked for me at least).
imagesc(app.ImageAxes,im,"HitTest","off");
% or
im = imread(imgName)
im.HitTest = "off";
In looking into this, I found the following posts helpful.
