Several Democratic incumbents in New York saw unusual challenges from more conservative candidates in Tuesday’s primary, with the opponents hoping to benefit from a demographic change, as an influx of immigrants is shifting some districts to the right.

Just over 149,000 people had cast their ballots as of 6 p.m., according to the New York City Board of Elections. That includes 44,611 votes that were cast during the nine-day early voting period that began June 17 and ended on Sunday — less than a quarter of the early-voting turnout two years ago, when candidates for mayor were competing in the primary.

There were contested primaries in City Council contests across the boroughs, district attorney races in the Bronx and Queens and, further north, a Council race in Buffalo that is a test of Black political power.

The City Council races are for a two-year term instead of the usual four years because of redistricting. Every seat on the City Council is up for re-election, but less than half of the 51 Council seats are being contested in primaries, and of those, 13 races feature more than two candidates — making ranked-choice voting, where voters can rank up to five candidates in order of preference, necessary.

Ranked-choice voting will not be used in the races for district attorney.

How Ranked-Choice Voting Will Affect the Results

The New York City Board of Elections will reveal the first-place vote totals each candidate receives on Tuesday; if one of the candidates in the 13 Council contests where there are three or more contestants draws 50 percent of the vote or more, a winner should be declared.

If no candidate hits the 50 percent mark, the board will use the ranked-choice system, but not until July 5. The board usually runs the first ranked-choice calculation seven days after the vote, but because that day falls on the Fourth of July, the tabulation will be delayed a day.

If necessary, additional ranked-choice tabulations will be held each week afterward, on July 11 and July 18, said Vincent Ignizio, the deputy executive director of the Board of Elections.

About 15,000 absentee ballots have already been filed, but additional absentee ballots can be received a week after Election Day as long as they are postmarked by June 27.

Under recent changes to state law, voters will also have an opportunity to cure or fix mistakes on their absentee ballots. The tentative last day to receive absentee ballot cures is July 17.

Because of the low turnout, Board of Elections officials don’t expect that more than three rounds of ranked-choice voting tabulations will be required.

Susan Lerner, executive director of Common Cause New York, a government watchdog group, said ranked-choice voting gave people more options. “We heard some voters in our 2021 exit polling say that because they knew they had the ability to rank, they actually paid more attention to more candidates,” she said.

Some Key Races to Watch

Central Harlem City Council Race

In Harlem, three moderate Democrats are running in one of the most competitive races in the city to replace Kristin Richardson Jordan, a democratic socialist who dropped out last month.

Ms. Jordan faced questions about her belief that the police should be abolished and about her far-left stance on housing development. Her name will remain on the ballot.

The three Democrats running to replace her have sought to distance themselves from Ms. Jordan. They are: Inez Dickens, 73, who held the Harlem Council seat for 12 years before joining the State Assembly; Yusef Salaam, 49, one of five men exonerated in the rape of a female jogger in Central Park in 1989; and Al Taylor, 65, who is serving his sixth year in the Assembly.

All three candidates gathered at Lenox Avenue and West 134th Street on Tuesday afternoon to try to woo voters. Ms. Dickens’s staff used a bullhorn, while Mr. Salaam’s team rang a bell every time a voter said they had ranked him first.

Chantel Jackson, an assemblywoman from the Bronx who grew up in Harlem, came out with her nearly 2-year-old son to hand out fliers for Mr. Taylor. Mr. Salaam and Mr. Taylor had cross-endorsed each other, asking voters to rank them first and second. Ms. Dickens was endorsed by Mayor Eric Adams.

The major issues in the historically Black neighborhood include the loss of Black residents, lack of affordable housing and a saturation of drug treatment centers and social service providers.

The candidates have struggled to differentiate themselves. All three say they would have supported a new housing development on West 145th Street that Ms. Jordan initially rejected because it was not affordable enough.

Ms. Dickens and Mr. Taylor have contended that their experience would make a difference, while Mr. Salaam, who moved back to the city from Georgia to run for the seat, has argued that it is time for a generational shift.

“Knowledge is power,” Ms. Dickens said while campaigning. “If you don’t have the knowledge, working in the system is difficult.”

Other City Council Races

Other City Council races to watch include one in Lower Manhattan where the incumbent Chris Marte, a progressive Democrat, is fending off a challenge from Susan Lee, a consultant; Ursila Jung, a private investor; and Pooi Stewart, a substitute teacher. All the challengers emphasize public safety and education and view Mr. Marte as being too far to the left.

In the Bronx, an incumbent, Councilwoman Marjorie Velázquez, is being criticized by some of her opponents because she backed the rezoning of Bruckner Boulevard in Throgs Neck to bring affordable housing to the area.

In southern Brooklyn, three Asian American Democrats are running in a newly formed district.

The candidates are Wai Yee Chan, the executive director at Homecrest Community Services; Stanley Ng, a retired computer programmer; and Susan Zhuang, the chief of staff for Assemblyman William Colton.

In a district that has swung to the right in recent years, the winner of the Democratic primary is expected to face a tough general election challenge from the Republican primary winner.

Vito J. LaBella, a conservative Republican and former Police Department officer, is facing Ying Tan, who works in senior services, in that primary.

New York City District Attorney Races

In the Bronx district attorney race, Darcel Clark, the incumbent, is running against Tess Cohen, a criminal defense and civil rights lawyer.

Ms. Cohen is challenging Ms. Clark from the left, arguing that the Bronx is lagging behind other boroughs when it comes to alternatives to incarceration and criminal justice reforms.

Ms. Clark has pointed out that she created a gun court program, which gives a second chance to young people who face gun possession charges and have no prior violent felony convictions.

In Queens, the incumbent district attorney, Melinda Katz, is facing a challenge from her right four years after she narrowly defeated a democratic socialist who wanted to abolish the police and end cash bail.

George Grasso, a former Police Department first deputy commissioner, has attacked Ms. Katz as being soft on crime, an accusation that Ms. Katz disputes, pointing to her focus on retail theft, gang takedowns and gun seizures.

Buffalo Common Council

In Buffalo, a Democratic primary contest features two prominent Black women vying for a Common Council seat in the Masten district, on the city’s East Side, where a racist gunman killed 10 people last May in a mass shooting at a Tops supermarket.

India Walton, a democratic socialist, rose to prominence in 2021 after defeating Mayor Byron Brown in a primary, only to lose the general election after Mr. Brown mounted a write-in campaign.

Her opponent, Zeneta Everhart, a former television news producer who works for State Senator Timothy Kennedy, is the mother of one of the victims of the Tops shooting, Zaire Goodman, who was shot in the neck but survived.

Both women have promised to address economic and racial inequities in Masten — a traditionally Black part of Buffalo and a seat of Black political power. Ms. Walton has been critical of Ms. Everhart’s connections to the Democratic establishment, including endorsements from the county Democratic Party and Senator Chuck Schumer.

Jesse McKinley, James Barron and Lola Fadulu contributed reporting.