SWEDEN
As of 21 January 2022 citizens of the Republic of Serbia who have a digital certificate of EU vaccination (EU Digital COVID-19 Certificate), issued by the competent authority in Serbia, can enter Sweden and do not need a negative test for COVID-19.
Please note that some vaccines available in the Republic of Serbia are not accepted in the Kingdom of Sweden.
At the present time, accepted vaccines are only the vaccines in accordance with the ordinance EU 726/2004 or approved by WHO for use in emergencies (source - https://polisen.se/en/the-swedish-police/the-coronavirus-and-the-swedish-police/faq/#laws):

Comirnaty (COVID-19 vaccin BioNtech Tozinameran)
Spikevax (COVID-19 Vaccin Moderna)
Vaxzevria (COVID-19 Vaccin AstraZeneca)
COVID-19 Vaccin Janssen
COVID-19 vaccin AstraZeneca/SKBio
COVISHIELD (Serum Institute of India COVID-19 vaccin)
COVID-19 vaccin BIBP/Sinopharm
CoronaVac (COVID-19 vaccin Sinovac).
COVAXIN (COVID19 vaccine Bharat Biotec)
COVOVAX (COVID-19 vaccine Serum Institute of India)
NUVAXOVID (COVID-19 vaccine Novavax).
Please note that the list does not include the vaccine against COVID-19 Sputnjik V.

The following categories of the unvaccinated persons from non-EU countries, including Serbia, may be allowed to enter Sweden, only if they are included in the mentioned exemptions:
• children under the age of 18;
• people with long-term resident status in Sweden;
• people with imperative family reasons;
• people in the transport sector;
• seafarers;
• people covered by Chapter 2, Section 10 of the Aliens Act (2005:716), for example diplomats and consular staff stationed in Sweden, and their families and staff;
• people who have been invited in a separate procedure by the Government Offices;
• people in need of international protection or with other humanitarian grounds;
These persons do not need a negative COVID-19 test result. The Swedish Police Authority reserves the discretion right to decide in each case, especially if the conditions for entry into Sweden are not met.