Which countries in Europe aren’t part of the Schengen Zone but still…

Can you write an appeal letter if you get rejected by the embassy for the Schengen Visa?

Yes you can always write an appeal letter no matter which Visa you apply for. In the appeal letter you write to the embassy you have to make sure that you have a strong reason to object to the embassy’s decision. You have to include your personal details, the reason your application got rejected and the reason you believe this decision is incorrect.