In a medium sized bowl, add the Greek yogurt and self rising flour, and mix well with a spatula until the mixture turns into a sticky dough. Form the dough into a ball. It will be tacky.
Cut the dough ball into 4 equal pieces. On a lightly floured surface, roll each dough ball out into an 8-inch long rope, then bring the edges together to form a bagel shape, pinching the ends of the dough together to close the circle.
Lightly grease the bottom of the air fryer basket with non-stick cooking spray. Place the bagels into the basket, leaving about an inch of space between each. Note: if your air fryer is small, you may need to cook the bagels in two batches.
In a small bowl, whisk together the egg and water. Lightly brush the egg wash over the top and sides of the bagels. Sprinkle toppings over the bagels.
Air fry the bagels at 350F for 10 minutes until risen and golden brown.
Remove the air fryer basket from the air fryer and allow the bagels to cool for 5 minutes. Remove the bagels, slice and serve warm, or cool completely then toast.