I have this small black ball in the corner of my tear duct for years. (photo)

Thank you for sharing your concerns and photo. The spot needs to be evaluated in person by an Oculoplastic Surgron with a slit lamp in order to give you proper guidance. Good luck,

It's important to consult with an eye care professional regarding any persistent growths or changes in your tear duct area. While a small black ball could be a benign condition like a cyst or a blocked tear duct, only a qualified specialist can determine the exact nature of the issue and the best course of action. Surgery may not always be necessary, as there are various treatment options available depending on the diagnosis. If you're concerned about this growth, make an appointment for a thorough evaluation to discuss your symptoms and potential treatments.

It is reasonable to have this assessed by an oculoplastic surgeon.  If appropriate, they can arrange to exicisionally biopsy the lesion.  It is considered a minor procedure with rapid recovery.  The American Society for Ophthalmic Plastic and Reconstructive Surgery maintains a regional directory on their website that can help you find an appropriately trained oculoplastic surgeon close to home.

these lesions usually are recommended to be removed, since there is difficulty with assessing if there is any change in the color or shape of them. My recommendation will be yes, you need to have it removed. 

  Like all pigmented lesions, or "spots," that come up out of nowhere, this one needs to be evaluated. Skin lesions need to be seen by a plastic surgeon or dermatologist, and lesions such as yours on or near the eye, must be evaluated by an oculoplastic surgeon. Find one and make an appointment right away. 

The black spot is most likely a benign growth (nevus) of the caruncle. These are most commonly benign but malignancies have been reported. These can be safely removed by an oculoplastic surgeon.

This lesion appears to be in area in your inner eye called the Caruncle.  It is very common to have cysts there, but occasionally cancerous growths may occur there.  Generally, this lesion can be removed by an oculoplastic surgeon, and depending on the size, may be able to be done in the office.  Definitely make sure a biopsy is sent for analysis to make sure it is nothing to worry about or that may require further treatment.  Good luck!

Generally pigmented lesions in this area should be checked by an oculoplastic surgeon, and removed. The removal may be done in an office setting with oral sedation, and topical anesthetic, followed by local anesthetic. Surgery in this area may lead to anxiety because of proximity to the eyeball, but with sedation and local anesthetic, you will probably be surprised that it is not as hard as you anticipate and the healing is swift. It's best to have the lesion removed, to know exactly what it is, and not have it there to cause you to worry. Best wishes.