BELGRADE : This summer, the governor of Serbia’s central bank is taking an aggressive position on a foreign currency: Trying to stop inventor Nikola Tesla appearing on Croatia’s coins.

       Though dead for 78 years, Mr. Tesla still raises temperatures between these two Balkan neighbors over which one has bragging rights to the pioneering electrical engineer, after whom Tesla Inc.’s electric vehicles were named.

       Mr. Tesla was an ethnic Serb and grew up in a part of the Austrian empire that is in modern-day Croatia. In 1884, at 28 years old, he emigrated to the U.S., where he pioneered how to make alternating current work on a grand scale, electrifying the world.

       For years, Serbia and Croatia have competed over Mr. Tesla’s legacy, naming buildings, monuments and streets after the inventor. In July, the Croatian public voted to have Mr. Tesla on the country’s new euro coins, when it joins the common currency, as scheduled, in 2023, in a poll held by its central bank. That would potentially put a Croation Tesla coin in the pockets of 340 million Europeans, further promoting the country’s claim to the inventor.

       Jorgovanka Tabakovi？, the governor of the National Bank of Serbia, promised to “take appropriate steps" with the European Commission, sparking retaliatory comments from Croatian officials. Mr. Tesla already appears on Serbia’s 100 dinar note and it has issued commemorative coins related to anniversaries.

       In Belgrade, where the ubiquity of Mr. Tesla’s name and image give him a profile typically reserved elsewhere for sport or pop stars, everyone has an opinion and that opinion is unanimous: Hands off, Croatia.

       It “would constitute the appropriation of the cultural and scientific heritage of the Serbian people, because it is indisputable that this famous scientist declared himself, throughout his life, as a Serb by origin and ethnicity," Ms. Tabakovi？ said in an email.

       Fighting for bragging rights of historical figures is nothing new. Alexander Graham Bell, who invented the telephone, is claimed by Scotland, where he was born and educated, Canada, where he later lived, and the U.S., where much of his work happened.

       Serbia’s rivalry with Croatia comes against a backdrop of conflict that sparked violence as recently as the 1990s, when the dissolution of Yugoslavia pushed ethnic groups into wars.

       Croatia’s minister of culture and media, Nina Obuljen Kor？inek, said there is no debate: Mr. Tesla was born in Smiljan, a village that sits in her country. She says that while Croats acknowledge his Serbian ethnicity, Serbs refuse to tip their hat to his birthplace.

       “I can’t even understand why they are complaining, it is so irrelevant," she said.

       But Serbia is complaining, and its central bank is leading the fight against what an official from the National Bank of Serbia calls the “forced posthumous Croatization of Nikola Tesla."

       Exhibit No. 1 in Croatia’s evidence: Mr. Tesla’s passport, carrying the coat of arms of the Kingdom of Croatia.

       Nonsense, says Serbia’s central bank, more used to debating interest rates and economic indicators. The passport clearly shows it was issued on behalf of Franz Joseph I, the ruler of the Austro-Hungarian empire, in which Croatia sat, the Serbian central bank official said. Croatia wasn’t an independent country at that time, she added, an idea Croatia’s present day government scoffs at.

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       Serbia rests its case on the idea that culture, ethnicity and self-identity are more important than location. Mr. Tesla was the son of a Serbian Orthodox priest whose family had a long history in the Serbian military.

       Croatia’s government points to comments Mr. Tesla said when visiting Zagreb in 1892, that it was his duty as “a native son of my country" to help the capital city.

       Two U.S.-based biographers contacted by The Wall Street Journal side with the Serbs. “When asked, Tesla would talk about being Serbian," said Bernie Carlson, a professor at the University of Virginia. Marc Seifer, who wrote a 1996 biography, said there is plenty of proof in essays that Mr. Tesla wrote that he saw himself as a Serb.

       Tesla’s CEO Elon Musk showed diplomacy in 2019 when he announced that his company’s cars were coming to the region: “Hoping to open in Slovakia, Croatia, Serbia and most of Eastern Europe early next year. Finally, we will do Nikola Tesla proud by having his cars in his countries of origin!" he tweeted.

       When Mr. Tesla died in 1937 his nephew shipped his belongings from New York to Belgrade, where they are currently displayed in a museum dedicated to him. His ashes crossed the Atlantic and are now encased in a golden orb that sits with religious reverence in a dimly lighted room in the museum.

       Those ashes have twice been embroiled in a tug of war between the Tesla Museum and the Serbian Orthodox Church, which wanted them displayed at Belgrade’s main cathedral.

       Croatia established its own Tesla Memorial Center, in the Smiljan home where the inventor was born. Ana-Marija ？olaja, a guide there, said she avoids talking about Tesla’s Serbian connections as much as possible.

       “I say only where he was born, what religion he was at that time (Orthodox), and then they can decide themselves where he was from," she said.

       Some see a lighter side to the spat. When news of Croatia’s currency plan became public, Serbian Helena Ivanov’s phone lit up with messages from Croatian friends trying to bait her. “Finally, a Serb on EU coins. Thanks Croatia," she texted back.

       But in Belgrade, souvenir seller Buki Miljkovic heard the words Nikola Tesla and Croatian and shook his head.

       “No, Serbian," he said of the inventor’s origins.

       Mr. Miljkovic does good business in Tesla T-shirts, mugs, refrigerator magnets and other souvenirs. Since Croatia voted to put Tesla on their coins, Mr. Miljkovic says he has increased his efforts to educate customers on the inventor’s origins.

       Aleksandar Filipovic Alfi paints pictures of Mr. Tesla, which he sells in central Belgrade. He has written a folk song about the inventor and intends to send a picture to Croatia’s prime minister so they can put a Serb-painted image on their coins.

       Ms. Tabakovi？, the Serbian central bank governor, says that Mr. Tesla’s relatives, along with other ethnic Serbs, were killed by Croatian soldiers during World War II, and that nationalists blew up a statue of the inventor near his birthplace and kicked out Serbs from the area in 1992. Ms. Obuljen Kor？inek, who unveiled a replacement statue in May, said Croats had also suffered in recent conflicts.

       The Serbian central bank has another edge, bank officials say—a current employee with a familiar name: Nikola Tesla.

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