With just three weeks to go until New York City's Democratic mayoral primary, former New York Gov. Andrew Cuomo is on track for a political comeback nearly four years after having resigned his governorship amid allegations of sexual harassment and inappropriate conduct -- but a Democratic socialist candidate continues to gain momentum among the crowded slate of contenders. All the while, incumbent mayor Eric Adams is staying off the primary ballot, and is running, instead, as an independent.

Whoever comes out of the June 24 Democratic primary victorious is more than likely New York City's next mayor -- nearly every borough in the overwhelmingly Democratic city voted for Vice President Kamala Harris in the 2024 presidential election, per election returns.

Cuomo announced his entrance into the race in March, saying in an announcement video that he was the best leader for New York City, which he said was "in crisis."

Cuomo's governorship was derailed after several women accused him of sexual harassment and inappropriate conduct. He resigned as governor in 2021, saying that the controversy would cause undue turmoil for the state, but has consistently denied the allegations and recently told the New York Times he regrets resigning. A New York state prosecutor dropped criminal forcible touching charges against Cuomo in 2022.

Cuomo also faced scrutiny for the state's tracking of deaths from COVID-19 in nursing homes during his tenure after reports that Cuomo and his team withheld from state legislators the true number of COVID-19 deaths at New York nursing homes.

Cuomo has defended his performance and the count, and an independent investigation in 2024 found that Cuomo's nursing home response policy was based on "the best available data at the time."

The Justice Department has begun an inquiry based off of a referral from Congress about Cuomo's handling of nursing home deaths during the pandemic, according to congressional documents and a source familiar with the matter. In a statement, Cuomo's spokesperson says the inquiry is "election interference."

"Governor Cuomo testified truthfully to the best of his recollection about events from four years earlier, and he offered to address any follow-up questions from the Subcommittee — but from the beginning this was all transparently political," Cuomo's spokesperson, Rich Azzopardi said in a statement in response to the inquiry.

His campaign has not been without roadblocks. The New York City Campaign Finance Board has withheld some matching funds from his campaign, saying that his campaign may have improperly coordinated with an independent group. Cuomo's campaign and the group separately maintain they did not break any rules or do anything wrong, and the campaign expects to eventually receive the full funds. And even still, at the end of May, Cuomo's team announced the campaign raised $3.9 million since Feb. 28.

And while other candidates have brought up the allegations and hit at Cuomo's record, no one attack seems to be sticking, and polling shows that Cuomo remains the front-runner.

Near ubiquitous name recognition and a gubernatorial record that resonates contribute to Cuomo's favorable polling, said Mitchell Moss, a professor of urban policy and planning at New York University.

Some of that record, Moss said, includes Cuomo's actions as governor such as rebuilding the beleaguered LaGuardia Airport and passing a law legalizing same-sex marriage in 2011, before it was legalized nationally.

Cuomo also already had a deep bench of support among Black voters and unions, Moss said, and many New Yorkers see him as aligning with their own values.

"People want a mayor they can connect to emotionally. And it's not just a set of policies you're picking. You're picking a person that you feel represents your values," Moss said.

For some people, the misconduct allegations against Cuomo are an issue, but many New Yorkers may be willing to look past it, Hank Sheinkopf, a veteran Democratic political strategist, told ABC News.

"They want somebody who appears nonchaotic, and they're prepared to forgive all his trespasses if he can make the city run," Sheinkopf said.

Among the other 10 candidates on the Democratic primary ballot, Zohran Mamdani, a state assemblymember and a member of the Democratic Socialists of America, is steadily inching upward in the polls and fundraising.

Mamdani is running on a progressive platform that includes a rent freeze for rent-stabilized apartments, eliminating fares for New York City buses and opening city-owned grocery stores.

He has gained major traction in recent weeks -- raising more than $8 million through donations and matching funds, Mamdani's campaign announced on March 24, and gaining buzz across social media with snappy TikTok videos and social media soundbites about his plans.

"Mamdani is the one to watch... He is fresh; the others are tired," Sheinkopf said. "The things he's saying have a populist appeal, whether they are realistic to achieve or not."

Sheinkopf also said Mamdani's ads are "very smart … he's captured the generational argument," and that the Democratic Socialists of America have effectively organized their support and outreach for Mamdani.

Yet Mamdani is nowhere near the household name that Cuomo is. And with early voting starting on June 14, the window for candidates to make their case for the job is closing fast.

Mamdani has also faced some scrutiny over the feasibility of some of his plans, as well as his views on Israel, given New York's large Jewish population. He has said that he supports boycotts and pressure on Israel over its conduct in the Israel-Hamas war, but frames that within his general "support for universal human rights", as he told The Forward in April, and he has emphasized policies to combat antisemitism. In May, Mamdani told a reporter that he supports Israel's "right to exist as a state." At a forum held by the UJA-Federation of New York and the Jewish Community Relations Council in May, he did not answer directly when asked if Israel has the right to exist specifically as a Jewish state.

Other candidates have struggled to break through including New York City Comptroller Brad Lander, city councilmember Adrienne Adams, former hedge fund manager Whitney Tilson and state Senator Zellnor Myrie.

Most of the candidates will face off head-to-head for the first time during the initial mayoral Democratic debate Wednesday evening.