In a bowl, stir together the crab, cream cheese, garlic, green onions, sesame oil, and salt until combined.
To assemble the wontons, place a shallow bowl of water on your work surface. Take one wonton wrapper, dip the tip of your finger in the bowl and wet two edges of the wonton wrapper. Place 1 1/2 teaspoons of the crab filling into the middle of the wrapper. Fold the wrapper over into a triangle and seal the edges securely. Repeat with remaining wrappers and filling.
Heat the oil in a dutch oven over medium-high heat. Add the wontons to the hot oil, working in batches, and fry 1-2 minutes until golden and crispy. Transfer to paper towels to drain. Repeat with remaining wontons.
Serve promptly with Thai sweet chili sauce, Sriracha, or soy for dipping.