According to the classic book :”Carrots love tomatoes” by Louise Riotte, a book on companion planting, the plants that HINDER potatoes are cucumbers, pumpkin, squash, sunflowers, and tomatoes. Looking further, the book states that potatoes grown near cucumbers are more likely to be affected by phytophthora blight.
The plants that are BENEFICIAL to potatoes are bush beans, cabbage (and brassicas), corn, eggplant, marigolds, and nasturtiums.
Reading further, horseradish can be planted at the edges of the potato plot and they are symbiotic to each other (potatoes and horseradish), and the potatoes are more resistant to disease, and are healthier. Apparently, horseradish is effective against the blister beetle, but not the potato beetle. Horseradish can be invasive, so it should be dug up at the end of the season.
The book notes to NOT plant melons near potatoes, but does not say why (info under “melons” in the book).
Peas grow well with potatoes.
“Watermelons are good to interplant with potatoes, especially if potatoes are mulched with straw.”
“Do NOT plant raspberries near potatoes, since they make potatoes more susceptible to blight”
“Orach should never be placed near potatoes since it has an inhibiting effect on their growth”
Pole beans: nothing mentioned either way, so these should be ok to plant in the fence around the potato patch.
All the above is from the same book. It addresses each veg, herb separately, so the info is spread out.