Pocket of Fat in Perioral Mound Area

Your single small posted photo does not allow a complete analysis of the situation. You will need a face to face examination with a qualified surgeon. If this small bulging fat is reducible by hand then it is shifted buccal fat. The solution then is removal of the buccal fat pad via an incision inside the mouth.

My response to your question/post does not represent formal medical advice or constitute a doctor patient relationship. You need to consult with i.e. personally see a board certified plastic surgeon in order to receive a formal evaluation and develop a doctor patient relationship.

You have a thin face.  I assume looking at that part of your face that you are unusually thin.  Your issue is not localized fat.  You are missing volume in the face.  You can consider this the chiseled look.  If you want something done, the answer would be to place hyaluronic acid filler to fill in around these muscles.

Surgical treatment for localized fat deposits can be difficult.  Although small liposuction cannulas can be used safely, the difficulty lies in getting a smooth, well contoured result. Often times, however, 'fat pockets' are really the sign of volume loss in adjacent areas.  It is difficult to tell with your photo, but it may be that you need more volume rather than less.  This can be easily determined with a consultation.