Count: 0 — There are no European countries whose English short name begins with the letter J. Check the United Nations list of member states, the CIA World Factbook, and Eurostat and you will find that every sovereign state with territory in Europe starts with a different letter; J appears in country names only outside Europe (for example, Japan, Jordan, Jamaica).
Accept that this empty result reflects history and language, not a data mistake. Country names in Europe derive from a mix of Latin, Germanic, Slavic, Romance and Turkic roots, and the letter J is comparatively rare as the initial letter in those English short names. Also include transcontinental states (those with territory in Europe) when validating the list; none of them begin with J either, so the criterion still produces no matches.
Consider near-misses and alternatives for readers who expect J-entries. Include Jersey or the Bailiwick of Jersey as a widely known Crown dependency, and note Jan Mayen as Norwegian territory, but exclude them as sovereign states under the stated rules. Consult authoritative sources — the UN member list, CIA World Factbook and Eurostat — for official country status, and expand the search to global country lists if you want examples of countries that do start with J.