No potatoes at all. A slightly unripe potato has a potentially dangerous poison. Better to avoid any peels no matter the variety or confidence it was ripe enough. Nothing moldy or rotten that you wouldn't eat yourself. Avocados also a no-no along with trimmings from any plant from the nightshade family (tomato, peppers, potato, eggplant).
I usually only feed trimmings from food prep from my kitchen. Carrot, squash peelings, mushroom stems, celery, lettuce. I use a ton of onions in my cooking but I limit those to the hens and put them in the compost bin instead. I heard onion can affect egg taste. My girls won't eat tomato scraps, but will fly into my garden and mow on my beet greens ARGH!!!