Emission map not working properly. {SOLVED}

Hi. This happens because uvs do not align with the image.There are some other things you need to fix
- open your blend, join both meshgroups;
- delete all vertex group beside the head one, delete uv_1, delete an existing color attribute, create a new one with these settings;

- select uv_0. The star's uvs are too close to the border of the area designated to hats. Select both uv island of the start with L, press S, make them smaller;
- UV - Export uv layout, set Fill opacity to 1;

- deselect everything in 3d view, choose Edge select, then Select - Select sharp edges, change angle to 80, Mesh - Split - Faces by edges;

- in 3d view hover over a glass bowl, press L, separate, give the glass cut 0000 and the other one 0001;
- save, import back in s4s;

- open your diffuse in photopea or photoshop;
- sample the yellow of the star, then select all of it, including the glow, and delete it. The glow reaches the space meant for necklaces;
- textures need to have bigger margins to avoid this. So you can expand the blue area;
- File - Open and place exported uv layout;
- Ctrl-click on the layer preview of the uv layout to select it, Select - Modify - Expand, 7 px;
- create a new fill layer and choose this yellow as a color;

- export or save this image as png;
- open and place a template, select the area for hats ( it must be 512x256), press C to crop, enter to confirm;
- delete the template, uv layout and the background, so that only the yellow fill layer remains;
updated file

Your item does not need to morph. Vertex painting it with black disables morphing. If the item does not morph, it does not need uv_1

When you added thickness to your mesh, it was extruded at 90 degrees angle. These new edges are sharp and should be shaded as such. They are in Blender but not in-game. To change that, you need to split these sharp edges. Select -Select sharp edges select all edges above a specified value. If you were to leave it at the default 30, some unwanted edges would be selected. Makes sense to get it closer to 90 degrees. You could also do the same thing with Edge split modifier, but this method gives you freedom to add or remove edges from the selection before splitting

Would need to look at your map to answer that

it is of the wrong size. It must be 512x256 specifically

it looks fine now, are you sure its emission map that is causing this problem? Just in case, make sure you're importing the new file, not the old one
If everything is as it should be, share the package file instead