In Serbia, we are not using term VAT number. All companies have tax identification number (in Serbian – PIB – poreski identifikacioni broj).
Every company, not depending is the company in VAT system or not, has tax identification number.
There is register of tax payers on Tax administration portal, where you can put certain tax identification number and check is the company in VAT system or not.
At the moment of writing this answer, that link is https://www.purs.gov.rs/sr/pravna-lica/pdv/registar.html
In every case, you can find it by searching on Google “registar pdv obveznika pretraga” and choose first result which directs you to website purs.gov.rs
If you want to find tax identification number of certain firm in Serbia, you can do it on Serbian Business Registers agency website or by searching Bisnode website. Bisnode has similar data, so you can find data about the company on that website.