Can Fat Near the Inner Eye Area Be Removed?

Yes, there are two parts to belpharoplasty.  First, the excess fat is removed or repositioned.  Second, the excess skin is trimmed.  Occasionally, patient only need one or the other - fat removed or skin tightened.  That is why we customize the procedure to the individual patient.  I hope this is helpful.

Eyelid surgery, or blepharoplasty, is a beautiful procedure that yields excellent results and should be custom tailored in every aspect to your individual goals, needs, and anatomy. 
From your perspective as a patient, this surgery is very stealth with relatively simple recovery. From the standpoint of your surgeon this is a very intricate, detailed and fun surgery to perform where assessment and planning are everything!
Blepharoplasty has come a long way and become much more modern in recent years, focusing more on long-term results than just on taking away as much skin and fat as possible. This modern approach yields a much more natural look with much more satisfying long-term results. 
Blepharoplasty will address sagging skin, displaced, bulging fat and excess muscle. Occasionally areas around the eyes, like the eyebrows and sometimes even cheeks, need to be addressed to give a harmonious and comprehensive result.
There are non-surgical alternatives to blepharoplasty, including laser resurfacing, fillers, brow lifting and others, but which of those are applicable to you will be dependent, and a discussion with your surgeon can help delineate those options.
To ensure you are receiving the highest level of care, seek out a modernly trained, new-school dermatologic surgeon, oculoplastic surgeon, facial plastic surgeon or plastic surgeon who is board certified and fellowship trained in one of these "core four" cosmetic specialties. Membership in organizations like the American Academy of Facial Plastic and Reconstructive Surgery help to identify a highly trained surgeon.
Cameron Chesnut
#realself500 Physician

It sounds like you may need some fat removal and perhaps some excess skin removed as well. You will need to be evaluated in person by a facial plastic surgeon who has expertise in blepharoplasty.  This would still be an eyelid lift procedure.  I hope this helps.

The upper and lower eyelid areas have fat pads that can contribute to a puffy appearance.  The inner fat pads of the upper and lower eyelids sound like they may be an issue.  This is usually addressed with an eyelid lift by reducing the amount of fat in those areas.  Visit with a couple of board certified plastic surgeons

Dr. ES

Focal fat deposits can be addressed with eyelid surgery.  Eyelid surgery is all about tailoring the surgery to your eye issues.  For some the little knuckle of fat at the inner corner makes them feel old and addressing this with surgery is straight forward and can make a big difference.