Carefully slice kernels from corn using a sharp knife.
Bring a large pot of water to a boil, and season with 1 tablespoon salt. Cook beans until crisp-tender, about 3 minutes; remove using a wire-mesh skimmer, and spread out on a baking sheet or plate to cool.
Melt butter in a medium skillet over medium heat. Cook scallions and celery seeds until scallions begin to soften, about 5 minutes. Add corn and 1 teaspoon salt, and cook until heated through, 3 to 5 minutes. Stir in beans and paprika. Season with salt and pepper, and cook until heated through, about 2 minutes.
Storage: Succotash can be refrigerated overnight. Reheat gently before serving.