Telephone country codes never begin with zero.
Country code +3, dialed as 00 3 from many places, is an incomplete code somewhere in Europe. You need one or two more digits to specify the country.
However, in some countries, 003 is a prefix for dialing international calls.
To avoid confusion, it is best to write an international telephone number in correct international format, beginning with the plus symbol and the correct telephone country code (e.g., +353 or +84), omitting any dialing prefix.
(The plus signmeans "insert your international access prefix here." From a GSM mobile phone, you can enter the number in full international format, starting with the plus sign. The most common prefix is 00, but North America (USA, Canada, etc.) uses 011, Japan uses 010, Australia uses 0011, and many other countries use different prefixes.)
Leichtenstein is telephone country code +423.
where is telephone country code 1816
Yes, the country code +003 is associated with Italy, specifically when dialing from certain countries. However, it is more commonly recognized as +39, which is Italy's international dialing code. The prefix +0039 may be used in some contexts to indicate the country code for Italy.
That is not a country code.
Country code +57 is Colombia.
Country code 52 is Mexico.
Fiji has telephone country code +679.
Gibraltar is country code +350.
Moldova is country code +373.
Slovenia is country code +386.
Vanuatu is country code +678.
Niue is country code +683.