So I absolutely love the concept of this character. A magic jar for a head, scarf and all, ready for an adventure. Makes me wish I'd thought of it first!
Anyway, I want highlight a few things here, because even though you wanted to fix the scarf, I think there is room for improvement all over. Some of it being technical improvements such as managing colours, overall value(contrast), and cleaner lines. And then some of its just understanding your concept and getting it to be more believable within your constraints.
I'll talk only about the latter as I thinks is the biggest issue here and the rest of it you can read about in tutorials over on these forums or over at Pixel Joints.
So the first time I looked at this I instantly understood what I was looking at, but found it hard to read each object on the character. I think the reason for this is simply because the objects, jar, scarf and other bits of clothing haven't been rendered to emulate their real counterparts properly. Obviously you aren't going for hyper realism, so the constraint is the limited palette and size. So keeping the Jar part in reference, here's what I do.
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-Firstly find a good reference. Using references isn't cheating and can it be anything, such as real life objects, pictures, concept art and even pixel art if you're really struggling. I just searched 'potion concept art' and found loads of good examples of jars with liquids in them. Like this one for example:
https://melodiaproject.files.wordpress.com/2014/10/melodia-potion.jpg- There's transparency, loads of highlights on the glass and even a hard contrast on the edges. Try to simplify what you see in your head and apply them to your object, taking into account the direction of light as well and how much you want to simplify things. Easier said than done, I know.
But that's just one part of the whole. You need to try and understand the other important things like how the jar actually stays attached to the rest of the body and how you make it look normal. And then make it work. The scarf goes a long way in making this look feasible because it blocks whats going on at the neck. Pretty cool
The issue comes in simplify things I think. And you seem to be struggling with this the most. I see it on the Jumper and on the jar, where you don't seem to understand how you're going to add detail to things, so you add a highlight and add it to the edges of the jar or add folds in the jumper, but what it actually ends up looking like is a blob of noise here and there. Also, neither make sense when thinking about light theory.
My advice, keep things simpler. Use large areas of colour for light and then try to think about where shadows would be cast, like under the chin or arm pits or a small and I mean very small amount under scarfs and other pieces of clothing. Rationalize the amount of shadow that would be cast in these areas. If you add detail and it doesn't look right, don't be afraid to remove it.
Last thing I want to touch on is outlining. Please don't out line everything. The metal on your boots has its own outline, so does the scarf, arms, gloves etc. Just don't.
Anyway, rant over. I made an edit to illustrate my points. That last point about outlines, please have a closer look at my edit in comparison to yours. Also, the changes I made in colour and proportion are purely by preference. Be careful with your colour choices btw, they're very dark and a lot of them are near identical. Also, I'm no pro, things could be better.
I hope that makes sense and helps