Preheat oven to 325 degrees F (165 degrees C).
Cook and stir chicken, onion, and garlic in a large skillet over medium-low heat until onion is tender, about 5 minutes. Mix in spinach. Cook, stirring often, until spinach is reduced and chicken is lightly browned, about 10 more minutes. Transfer mixture to a bowl and combine with ricotta cheese, Parmesan cheese, and butter; mix until filling is creamy.
Unroll crescent roll dough and pinch 2 triangles together to form a rectangle of dough; repeat with remaining dough to make 12 rectangles. Place about 1 tablespoon of chicken filling onto the center of each rectangle and fold the corners together to make balls. Arrange balls on a large baking sheet.
Bake in the preheated oven until filling is heated through and puffs are golden brown, about 12 minutes.
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