As the subject states.
I cannot select it but have found that by closing down one layer it disappears but even taking all the work in that layer to a new layer it reappears. There is NO ENTRY for an ellipse under this layer.
Does it have a fill or stroke?
No fill or stroke just a small but evident circle.
no effects applied in any instant just fills and strokes. Just rechecked for each object top confirm.
Maybe you could share the file (or the part with the problem) so we can have a look at it?
CC filesharing, Dropbox, Google, WeTransfer...
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It could be an effect applied to one of the objects on that layer. Effect > Conver to Shape > Ellipse...