Sorry, I don't know Mill, but the way "connotation" is used in ordinary language, it would be the sort of thing Frege calls "coloring", among other things. Aspects of meaning that don't affect reference, the truth value of assertions a word is used in, and so on. Connotations are at least usually public, rather than just private associations, and Frege definitely wants sense to be public, but may not affect how reference is determined. (Maybe there's a different connotation for "the President" and "the Prez", but not the kind of difference that would change the truth value of sentences I used those words in.)

The analogy he gives is this: when you look through a telescope, there's the object you're looking at (reference), the image of the object on the mirror, viewable by whoever uses the telescope (sense), and then there's the entirely private image formed on your retina.

Fishing for assignment answers. It's a very specialised topic, you'd be better off doing your own research! And good luck with it.