Which Laser is the Best Applicable to Rid Under Eye Bags?

Almost impossible to answer with out photos and/or an exam. Although you can camouflage the problem in certain cases with fillers, a blepharoplasty is generally recommended.
Patients who would benefit from a blepharoplasty include those who experience:
• Excessive, sagging, or wrinkled upper or lower eyelid skin.
• Excess upper eyelid skin that interferes with vision.
• Loss of your natural upper eyelid crease
• If you have puffy pouches of fat in the upper or lower lids that create a tired or aged appearance.
• Orbital Rim Show: visibility of the bone under the eye sometimes contributing to a dark ring or shadowing.
Normally, everyone has a small amount of fat around the eyes. If the quantity of fat increases or the local tissues stretch and weaken, the fat begins to bulge producing “bags.” Occasionally this bulging is seen in young patients and is an inherited family trait, and not a result of aging. These changes have a profound effect on one’s appearance giving a tired or haggard appearance. An attractive face with these early signs of aging can affect a patient’s self-image, attitude and sense of well-being.

Without seeing your photos I can only guess that your eyelids are much like many of my blepharoplasty patients. Even at a young age, bulging fat from within the eye socket bulges the ovelying skin and can make you look tired. There are no lasers that can be used to selectively remove fat and blindly liposuctioning within  your eye socket ? you can understand why that's not done.

Precise removal of the fat under direct vision by a surgeon is the only long lasting solution. This can be done without any external incissions, takes about 30 minutes and is essentially painless.The procedure is called a transconjuncitval lower lid Blepharoplasty.  Fillers can be used as a temporary alternative to make the skin around the eyebags more full ,thereby camouflaging the underlying problem. Have a look at the video below and see if your eyelids have similar features to the patients in our video who had the surgery

Lasers applied externally to the skin, including the pulsed dye laser, will have no effect on under eye bags.  A pulsed dye laser can potentially be used to treat under eye blood vessels if they are small capillaries.  Under eye bags are due to protrusion of fat, and these either need to be surgically addressed or sometimes a filler can be used under the bags to help hide them.