The Kayser Fleischer ring is a band of copper laid down in Descemet's membrane at the rim of the cornea, seen as a golden brown to greenish circle, best caught on slit lamp examination. So the right answer must be a copper overload state.
That state is Wilson's disease. A faulty ATP7B copper transporter stops the liver from clearing copper into bile, and the metal piles up in liver, brain and cornea. The corneal deposit is exactly the KF ring. Clinically the disease shows liver dysfunction, movement and psychiatric problems, low ceruloplasmin and high urinary copper, with the $KF\ ring$ as the eye giveaway.
The distractors fall apart on chemistry. Pterygium is just a conjunctival overgrowth with no metal involved. Hemochromatosis is an iron loading disease, the wrong metal entirely. Menkes kinky hair syndrome is copper deficiency, the mirror image of Wilson's, so it cannot deposit copper rings.
The copper trail leads straight to Wilson's disease.
\[\boxed{\text{Wilson's disease}}\]