Peel the potatoes and place in a bowl of water until ready to shred. The water will help keep the potatoes from browning.
Cut the stems off of the jalapeños then slice in half and remove the seeds.
Using a food processor or a grater, shred the potatoes and jalapeños together. Place inside of a kitchen towel or cheese cloth and squeeze as much liquid as you can out of the potatoes.
In a mixing bowl, fold together the cream cheese, cheddar, and eggs. Add in the shredded potatoes and jalapeños, bread crumbs, and salt.
In a medium heavy-bottomed pan over medium-high heat, pour in about 1/4 inch of the oil. Once the oil is hot (a drop of the batter placed in the pan should sizzle), use a heaping tablespoon to drop the latke batter into the oil, cooking in batches of 3-4 latkes. When the edges of the latkes are brown and crispy, around 5 minutes, flip using a spatula or two forks. Cook until the second side is browned. Transfer the latkes to a paper towel-lined plate to drain and sprinkle with salt while still warm. Repeat with the remaining batter.
Blend the sour cream, jalapeño, and salt together in a food processor, or chop the jalapeño and add to the sour cream with a sprinkle of salt. Top the latkes and serve.