Stir together flour, salt, and baking power. In a separate bowl, mix together pumpkin puree, maple syrup, milk, egg, and vanilla. Thoroughly mix in dry ingredients.
Add 1 cup coconut oil into a large frying pan. Heat over medium. When the oil is hot, add about ¼ cup of batter in small circles/patches to make fritters (about 3-4 will fry in the pan at once). Cook each about 3 minutes per side. Flip and cook the other side for 3 minutes. Remove from pan.
Add the remaining coconut oil to the pan. Repeat with the remaining batter and fry the second batch of fritters.
Allow fritters to cool on a baking sheet lined with parchment paper.
For glaze: in a small mixing bowl, beat cream cheese until smooth. Add powdered sugar, a little at a time and continue to beat until fully incorporated. Mix in vanilla, pumpkin pie spice, maple syrup, and milk. Allow the pumpkin fritters to cool until only warm, then drizzle overtop.