Combine eggs and milk, stirring until well blended.
Combine flour, 1 teaspoon salt, and 1/2 teaspoon ground red pepper in a shallow dish. Dredge fillets in flour mixture; dip in milk mixture, and dredge again in flour mixture.
Pour oil to a depth of 3 inches into a Dutch oven; heat to 360°. Fry fillets 6 minutes or until golden; drain on paper towels. Keep warm.
Peel fresh shrimp, and devein,if desired.
Melt butter in a large skillet over medium heat; add shrimp and garlic, and cook, stirring often, until shrimp turn pink. Remove shrimp, reserving drippings in skillet.
Stir vermouth into reserved drippings; bring to a boil, and cook 1 minute. Add whipping cream, 2 tablespoons green onions, lemon juice, remaining 1/4 teaspoon salt, and 1 to 2 teaspoons ground red pepper; cook, stirring often, 12 to 15 minutes or until sauce is thickened.
Place catfish on a serving plate; drizzle with sauce. Top with shrimp and ham; sprinkle with remaining 2 tablespoons green onions. Garnish, if desired.