I hold Indian Passport and I have transit at Belgrade airport to reach Zurich.
Do I need a transit visa?
I am residing in Singapore so I will be travelling from Singapore to Belgrade to reach Zurich. Transit hours is about 1 hour 10 minutes.
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You won't need a visa transiting through Serbia.
According to Timatic:
Serbia - Transit Visa
The following are exempt from holding a visa:
A max. stay of 90 days for holders of a double or multiple entry visa issued by Switzerland, USA or an EEA Member State . The visa must be valid for the total length of stay.
A max. stay of 90 days for holders of a single entry visa issued by Switzerland, USA or an EEA Member State . Serbia must be the first point on entry. The visa must be valid for the total length of stay.
Transiting without a visa is possible for:
Holders of confirmed onward tickets for a max. transit time of 24 hours.
So given that you have a visa to Switzerland you don't need a visa.
I don't see any information whether transit visa required or not from the official websites (see below) to change planes within the airport. Did you check with the airline? FYI, Serbia is not a schengen country.
Serbia tourist page says
In order for a transit visa to be issued, travellers must have a visa for the country to which they are travelling after transit through Serbia.```
Also official foreign ministry website
For the issuance of a transit visa, you should have an entry visa for the country you are entering after the Republic of Serbia. In case a visa is not required for that country, you will be asked to present other documents explainning the purpose of your visit there.``
This means you have to show tickets, visa and passport and purpose of visit. Please check below link: