The Alternative for Germany, polling at over 40 percent for months in Saxony-Anhalt, even has its sights on winning its first-ever state government, although this is far from assured.
Polls opened at 8:00 am local time (0600 GMT) and some 1.7 million voters have until 6:00 pm (1600 GMT) to cast their ballots, with first projections expected shortly after.
The small state is now ruled by the centre-right CDU of Chancellor Friedrich Merz in coalition with two smaller parties, and its state premier Sven Schulze hopes to build again a multi-party coalition to cling to power.
All other major parties have so far maintained a "firewall" of non-cooperation with the AfD, whose Saxony-Anhalt branch is categorised as "right-wing extremist" by Germany's domestic intelligence agency.
The AfD's top candidate Ulrich Siegmund -- a telegenic 35-year-old who is feted like a rock star at campaign events and has a large social media following -- has confidently predicted gaining an absolute majority.
"It was the others who erected the firewalls," he told Bild daily. "If no one wants to work with us, then we'll just have to do it alone."
Such a scenario would shake Germany, a country that has long been at pains to atone for its dark history of World War II and the Holocaust and which has so far kept extremist parties in check.
A strong AfD win would also heap pressure on Merz, who has vowed to reboot a stagnant economy and restrict irregular immigration, but has seen his party beaten by the AfD in national surveys too.
"If the AfD wins in Saxony-Anhalt, Merz's critics will become even more vocal, and calls for better leadership will become impossible to ignore," said political scientist Wolfgang Schroeder of Kassel University.
However, Schroeder also said he does not expect Merz to be ousted, given the current absence of a strong rival candidate: "As far as I can see, there is no alternative chancellor."
'Remigration and deportation offensive'
Siegmund has vowed to topple a "domino" on Sunday and lead a political revolution from the small state of 2.1 million people that propels the anti-establishment party to national victory in 2029.
The AfD's key campaign promises include a "remigration and deportation offensive", a ban on LGBTQ pride rainbow flags at public schools, and an end to new wind farms.
The party has also tapped into a sense of nostalgia for communist East Germany and lingering resentment about an enduring wealth gap with the West decades after the 1989 fall of the Berlin Wall.
The prospect of an AfD state government -- while eagerly awaited by many voters -- has sparked alarm among mainstream parties and minority groups.
Thousands of the AfD's opponents joined a "festival of democracy" rally in Magdeburg on the eve of the vote.
The German Economic Institute warned the AfD's immigration policy would be "ruinous" for the state whose population is already ageing and shrinking and highly reliant on foreign-born workers.
Others have voiced fears an AfD-run state security apparatus could leak sensitive information to Russia.
The Kremlin "makes no secret of the fact that the AfD is the most important instrument for destabilising Germany for (Russian President Vladimir) Putin," Thuringia state interior minister Georg Maier told the Handelsblatt daily.
The latest poll, released Thursday by public broadcaster ZDF, gave the AfD a commanding lead of 41 percent.
The CDU got 23 percent, the centre-left SPD 8.5 percent and the Greens six percent, while two smaller parties failed to cross the five-percent hurdle to reenter parliament.
A similar result may allow a scenario where the CDU and others form a minority government with ad hoc support from the far-left Die Linke party, which polled at 11.5 percent.
In the final stretch of campaigning, a social media video stoked fears about mail vote fraud, with claims of manipulation at an elderly care home that were denied by state authorities.
Germany's parliamentary speaker Julia Kloeckner dismissed AfD speculation of voter manipulation, speaking to news weekly Der Spiegel.
"Questioning elections without concrete evidence appears to have one goal," she said, "to sow distrust in our rules and to accept the results only if the outcome suits".
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