Combine the paprika, cumin, and coriander. Place cut chicken strips in the medium bowl and toss with 1 tablespoon of the spice mixture.
Heat the olive oil in the pot over medium heat. Add the chicken and cook until browned, about 3 to 4 minutes. Transfer to a plate.
Add the onions and garlic to the pot and cook, stirring, until softened, about 5 minutes. Add the saffron, cayenne, cinnamon stick, and the rest of the spice mixture. Cook, stirring, for 1 minute.
Add the broth, squash, and the chicken. Cover and bring to a boil. Reduce heat to low and simmer, uncovered, for 10 minutes.
Add the mushrooms and carrot and simmer until the vegetables are tender and the chicken is cooked through, about 5 minutes. Discard the cinnamon stick. Stir in the lemon juice. Ladle the soup into bowl and garnish with the mint.