What is this pocket of fat and how can I get rid of it? (Photo)

This may represent the buccal fat pad. It can be removed via a small intraoral incision under IV sedation in an office setting. An in person exam should help elucidate this better.

Each individual persons facial characteristics is primarily determined by their facial skeleton bone structure.
Soft tissues tend to be very consistent from patient patient though there are exceptions. it is unlikely you have an abnormal fat distribution.
To make accurate facial assessments we need quality pictures taken the way plastic surgeons take facial before and after pictures. angles need to be straight the entire face needs to be included and the patient should avoid facial expressions in the picture.
I don’t think you need fat removal and honestly based on your post it’s hard to see what the problem is.
With facial expressions contours are formed because of the pull intentions of muscles a facial expression. these can change facial contour and should not be treated.
We make assessments in a static position without facial expression to get a baseline understanding of what someone’s face looks like.
Issues related to facial expression can sometimes be manipulated with Botox type treatments but these are limited to some degree.
Having subcutaneous fat removed from your face if fat distribution is not the problem can lead to very different results than you had hoped for.
Recognize that Liposuction is a permanent and in many ways irreversible operation.
To get an accurate assessment and better understanding of treatment options I suggest having multiple in person consultations with local board-certified plastic surgeons.
Consult with enough providers to get a good sense of who seems to know what they’re doing and who doesn’t.
Unless there’s a clear and obvious treatable condition surgery should probably be avoided.
Best,
Mats Hagstrom MD