How can I remove fat pouches present underneath my bottom lip? (photo)

This is your natural lip tissue which is supporting your very full and symmetrical lips. I strongly suggest avoiding any treatment to remove it. I recommend scheduling a consultation with a board-certified cosmetic dermatologist who is an expert in facial rejuvenation techniques if you have specific questions regarding your facial anatomy. In my practice, we combine dermal fillers with over 45 lasers, Botox, and other treatment modalities to customize treatments for the unique needs of each of our patients. Good luck!

I appreciate your question and photo. I agree with the other surgeons in this thread that think your lips are a beautiful shape without any anatomical abnormality to address. If you tried to adjust this area, chances are the results would not look as aesthetically pleasing as your current appearance. 

Actually, your lips look nice and full and I would not make any adjustments to the white portion along the side of the lip. This is likely the orbicularis muscle which supports your lower lip and helps to maintain the shape and fullness.