I am unable to change my AppleID region from Switzerland to Serbia due to an unpaid order(s) and I no longer have access to the Swiss payment method.

Refer to this document for ways to contact Apple ➞ Choose your country or region - Official Apple Support

Select your country (also look for "other" regions), then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service by telephone ➞ Contact Apple for support and service - Apple Support

for "Billing and subscriptions" support, click here --> Subscriptions and Billing - Official Apple Support

Yeah, I hear you say, "I have tried that". Well that was the formal reply.

To put on my creative, "Can we find a solution that might work?" hat: Do you have a friend in Switzerland who could purchase a Swiss Apple gift card? You could then add this to your account which appears to still be set to Switzerland. The outstanding balance would be deducted and you might likely have to add too much and would have to ask Apple to keep the remainder, but at least it would clear your account. Alternatively, if you have a friend who really trusts you and would be willing to let you use their credit card, you could add that so the outstanding balance would be paid with a Swiss payment method. You could then change country.

The article Change your Apple ID country or region - Apple Support describes how to change your Apple ID country or region, and the requirements and results of doing this.

You may encounter various issues and here is how to deal with them:

● Subscriptions

Make sure you have canceled all your subscriptions (see: If you want to cancel a subscription from Apple - Apple Support ). Wait for any memberships, pre-orders, movie rentals, or season passes to complete. Items will still be active until their expiration date. You need to contact Apple and request any ongoing items you have be ended immediately if you do not want to wait until they expire naturally.

● Remove all your Apple Account balance

- In the main change country article Apple only proposes a single way for you to clear your balance. That is to contact them and ask them to keep it. Apple offers this specific link for that service --> https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0998&symptom_id=20198

- Another still viable way is to add a credit or debt card as a payment method to your Apple ID and buy items just in excess of your remaining Apple ID balance. This will use up all the balance and any excess will get charged to the card, leaving nothing in your account.

● Pending purchases and refunds

If you have pending purchases, or refunds in the process of being returned to you, you will have to wait until these clear.

● Leave or disband any Family Sharing groups.

Refer to Leave Family Sharing - Apple Support

For items where you need to contact Apple to resolve an issue:

Click here --> Choose your country or region - Official Apple Support Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

See a list of Apple phone numbers around the world. Click here --> Contact Apple for support and service - Apple Support

or:

If you are no longer in the country that holds the balance, try filling out this form: Media Services - Contact Us - Official Apple Support