If using frozen wrappers, thaw according to the package. Keep them covered while working. Set out a rack and a rimmed pan to catch drips.
Lay a wrapper like a diamond. Roll a banana half lightly in the sugar and place it across the lower third with one jackfruit strip. Fold the bottom corner over the fruit, fold both sides inward and roll snugly. Dampen the last corner with water and seal. Repeat.
Heat 1 inch of oil to 350°F (175°C) in a heavy pan. Fry in small batches, seam-side down first, turning until golden and crisp all over, about 3–5 minutes per batch. Let the oil return to temperature between batches.
Drain on the rack. Let stand a few minutes before eating; the fruit stays hot inside the shell.