Short answer
Store all potatoes in a completely sealed, cat-proof container inside a closed pantry or cupboard. Never leave them in a bowl on the counter or in an open bag, as the green skin and sprouts contain solanine, which is highly toxic to cats. Regularly check your potato stash and immediately discard any that are green or sprouting. Teaching a solid 'leave it' command can also be a helpful backup, but the safest approach is always secure storage out of sight and reach.
Green or sprouted potato — Food safety facts
Do not feed · Cats · full breakdown on the linked food page
Green skin and sprouts contain solanine, which causes vomiting, tremors and heart problems.
The full verdict, portion guidance and serving notes are collected on the Green or sprouted potato food facts page.