How to export textures of meshes?

Hi, I have been trying to export the textures of a mesh in blender so I can apply it to the mesh in Roblox Studio. I imported a color palette into the blender UV space, and then positioned the vertices of the mesh after UV unwrapping them in the correct places.
It looked something like this:
TextureWithVerts
The problem however, is that whenever I save the image of the texture, it does not save the vertices and just the default color palette:
Texture
I tried searching up youtube videos and followed tutorials but the texture was still messed up upon import. If anyone knows what I have done wrong or the correct method of exporting textures, please let me know.

UPDATE:

I managed to successfully export and import the texture, however the leaves which were green in blender are now red.

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If you are doing this all in blender. You can export the mesh with the texture included into roblox studio. If you have a texture applied to the mesh, just export it as a fbx or obj.

If you are just trying to export the texture only, go to the UV editting page that has the texture, press image, and save as:

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I tried exporting the texture by doing that, I told you, it only exports the color palette.

The topic has been updates with a new issue.