Set grill to medium-high heat. Grill the corn with the husks on for 20 minutes, rotating every 5 minutes, until outsides are lightly charred. In the last 5 minutes, add the jalapeño peppers and cook until lightly blackened.
Remove the husks and silks from the corn and cut the kernels off the cob. Seed and mince the jalapeño peppers, reserving seeds if more heat is desired.
In a large bowl, mix corn, jalapeño, mayonnaise, sour cream, cheddar, and pepper jack cheese until well combined. Add smoked paprika and kosher salt. Taste for seasoning and adjust if desired.
Chill until ready to use. Serve with classic potato chips or tortilla chips.