Does apple send products to Serbia? (Serbia Doesn’t have official Apple store, but have auth. stores)

Apple do not ship across borders. In your case you should buy from an Authorised store. Remember, with iPhones, the warranty is not international so if in the unlikely case that it develops a fault, you would have to send it back to the country where you bought it from if you bought it yourself while travelling.

What are you looking do? Sounds like perhaps buy one as a gift and have Apple ship it to Serbia? If that's the intent, then no. If you're looking to have a device sent to an address in Serbia, then it might make more sense to buy through a Serbian authorized reseller.