Open can and drain excess liquid. Place salmon in a large bowl. Remove salmon bones, if desired.
To the bowl, add pumpkin, coconut flour, tapioca flour, and pesto. Gently stir to combine.
Divide salmon mixture into 8 portions. Roll each portion into a ball in your hands and flatten into a patty shape. If mixture is too wet to form a patty, add an additional 1 tbsp tapioca flour.
In a large skillet over medium heat, heat coconut oil for approximately 2 minutes.
Cooking in batches, carefully add formed patties to the hot oil and fry for 3 to 5 minutes per side, until patties are cooked through and edges are browned and crispy. Flip patties only once or twice to ensure they do not lose their shape.