What is the fat in the corner of your eye?

Do you mean the fat in the inner corner of the upper lids?  That is fat that has moved forward in the orbit, so it is visible below the skin.  This is a common aging change.  It can be removed surgically. See an oculoplastic surgeon for this.

It would be unusual for fat to herniate and be visible in the corner of your eye.  If it is a concern see an ophthalmologist.