Both mayonnaise- and vinaigrette-based potato salad work for fritters. Just make sure it has a balance of starchiness, savory flavors, and vinegar or citrus for some acidity.
Add 1 egg and ½ cup of breadcrumbs for every 2 cups of potato salad. Then, mix it all up, let it rest for 10 minutes, and see if it's sticky enough to make a ball.
If you use a mayonnaise-based salad, you might not need the egg or breadcrumbs as a binding agent. Test it by scooping out a ball with a spoon to see if it forms a sticky sphere.
Lightly mash the potato salad with a fork or potato masher, scoop it into spheres, flatten them, and dredge them in breadcrumbs. Use panko or grated stale bread for extra crunch.
In a hot pan, you can fry small batches of the fritters in olive or avocado oil. Brown the patties on both sides over medium-high heat, and drain them on a paper towel.
You can also bake a large batch on a sheet pan lined with parchment paper. For extra crunch, apply some baking spray or oil from a spray bottle before popping them into the oven.
Fritters also come out great in an air fryer. Serve them with sour cream or Greek yogurt, and top with chopped fresh chives or sliced scallions, just like potato pancakes.