Combine the snapper and lime juice in a bowl and macerate in the refrigerator for 2 hours. Drain the juice and put the snapper in a bowl. Add the tomato, onion, cilantro, olive oil, chile, and season with salt and pepper.
To make the sopitos:
Combine the masa harina, water, and salt in a bowl and mix well to form a dough. Let rest for at least 20 minutes. Form the dough into small, shallow flat-bottomed cups, each one about 4 inches in diameter and 1/2-inch tall. Heat about 3 inches of corn oil in a saucepan and fry the sopito disks until golden. Keep warm.
Fill the sopitos with the ceviche mixture. Garnish the top of each sopito with julienne radish and micro cilantro. Garnish the plate with radish halves seasoned with salt and olive oil.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.