Grate the potatoes on the large holes of a box grater and rinse with cold water in a colander. Strain well and squeeze dry in a towel. Transfer to a bowl and add the chopped chives and egg. Mix well to thoroughly combine, then sprinkle with the flour, 3/4 teaspoon salt and a few grinds of pepper. Mix to combine.
Heat about 1/8 inch of oil in a large nonstick skillet over medium-high heat until shimmering and hot. Working in batches, spoon rounded tablespoons of the mixture into the skillet and flatten each to make thin pancakes. Cook, turning once, until golden brown on both sides, 2 to 3 minutes per side. Transfer to a paper towel-lined plate to drain.
Spoon a little bit of sour cream on each pancake followed by a dollop of the pepper jelly. Garnish with the chive segments and serve.