Combine water, chicken broth, and rice in a pot; bring to a boil. Reduce heat and add ginger. Cook, stirring occasionally to prevent sticking, until rice is fluffy, about 1 hour 30 minutes. Stir in preserved eggs.
Combine cod slices, rice wine, sesame oil, soy sauce, and white pepper in a bowl. Add to the pot; cook until tender, about 5 minutes. Stir salt in gently.
Ladle congee into serving bowls; garnish with green onion.