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Hello. Thanks for the question.
The most common cause of this discharge in a cat, is a corneal ulcer or scratch to the cornea. These are commonly due to trauma or a viral infection (Herpes) in the eye. Either way, we typically treat them with an antibiotic drop and pain meds.
A Fluorescein stain test will be done to make sure there is an ulcer. If the test is normal, then they may just start him on some anti-inflammatory drops in case of an allergic type conjunctivitis.
I hope this helps, let me know if you have any other questions.