Best/affordable procedure to get rid of fat under mouth? (photo)

This is not an area that carries fat, more likely this has to do with the masseter of the lower lip and is something that we wouldn't alter as it can lead to distortion of the mouth especially when activating those muscles.

There could be other alternatives to conceal this, by increasing the projection and width of the chin through Fat Injections, Genioplasty or implants. Non-surgically speaking, you could use fillers.