Whether they stick with Democrats or continue their shift to the right, Asian American voters will help decide competitive races on Nov. 7.Two years ago, many Asian American voters in New York City demonstrated their political muscle by voting for Republicans in traditional Democratic enclaves, voicing their concerns about crime and education while sending a warning signal to Democrats.The message was quickly received.“Our party better start giving more” attention to Asian Americans and Pacific Islanders, Representative Grace Meng, a Democrat and the first Asian American elected to Congress from New York, wrote on Twitter at the time, using more colorful language to drive home her point.Asian Americans’ growing political clout was also seen in the New York City Council that year, when a record five were elected, including the first Indian American and Korean American members.As the Nov. 7 election nears, in which every City Council seat will be up for grabs, Asian Americans’ strength — as well as their political alliances — will be put to another test.Several Asian Americans are running in this year’s Council races, most notably in a so-called Asian opportunity district in Brooklyn that was created last year as part of a once-a-decade redistricting process to reflect the community’s growth.“I’ve never seen so many Asian Americans running for office,” said Councilwoman Linda Lee, the Democratic incumbent from Eastern Queens who is running against Bernard Chow, a health care benefits adviser and a Republican, in another race where both major party nominees are of Asian descent.Councilwoman Linda Lee, a Democrat, was one of a record five Asian Americans to be elected to the Council in 2021.Janice Chung for The New York TimesWith Asian American influence clearly on the rise, Democratic and Republican leaders are strategizing over how best to capture their votes.Leading Democrats, including Attorney General Letitia James, have expressed concern that the party is losing touch with Asian American voters, especially in southern Brooklyn and Queens, in part because it has not capably battled “misinformation and disinformation.”Republicans, meanwhile, have cast the wave of migrants who have recently come to New York in a negative light, hoping to attract more conservative Asian American voters by deploying a similar strategy as last year, when they amplified fears of crime as a wedge issue.Focusing on such issues may attract Asian American swing voters who may not otherwise be inclined to “completely flip Republican,” said Jerry Kassar, chairman of the state Conservative Party, but are “willing to cast their vote for Republicans.”The Queens district being contested by Ms. Lee and Mr. Chow includes the Hollis, Douglaston and Bellerose neighborhoods and is 45 percent Asian. Like in many districts with significant Asian American populations, Democrats and Republicans there often hold similar stances on the top line issues of public safety, education and the arrival of migrants.Both Ms. Lee and Mr. Chow opposed the placement of a tent complex for 1,000 men in the parking lot of Creedmoor Psychiatric Center in Floral Park, Queens, but Mr. Chow contends, incorrectly, that the migrants are here illegally.“I earned my way in,” said Mr. Chow, who emigrated from Hong Kong to the United States to attend college before becoming a citizen.In July, while Ms. Lee was holding a news conference in a building near the psychiatric center to oppose the tent city, on the grounds that the infrastructure in the area wasn’t sufficient to provide for 1,000 additional people, Mr. Chow was outside with protesters, some who held up signs that said “send them back.”Mr. Chow said opposing the shelter was not enough and that Ms. Lee could have done more, including standing with protesters to demand change. Ms. Lee said she spends time with voters explaining what she has done to mitigate issues around the tent city but rejects the xenophobic comments made at some of the rallies.“Asylum seekers come here from horrible situations, and they want to work,” Ms. Lee said.In northern Queens, Asian American voters are being courted in a rematch of a 2021 election in which the Republican candidate, Vickie Paladino, narrowly defeated Tony Avella, a Democrat.Councilwoman Vickie Paladino, a Republican, works with three surrogates, including Yanling Zhang, right, to better reach Asian American voters.Janice Chung for The New York TimesMs. Paladino often knocks on doors with one of three Asian American surrogates, and Mr. Avella has prioritized printing campaign fliers in Mandarin and Korean, reflecting the fact that Asians now comprise 38 percent of the district.“I think the Asian community is finally coming into its own,” Mr. Avella said. “For decades, they were not listened to. Now, they can turn an election.”Asians are the fastest growing group in New York City, according to the 2020 census, which shows that New York City gained 630,000 new residents, 55 percent of whom are Asian, in the previous decade. “Asian Americans are a waking giant,” said Trip Yang, a Democratic consultant who is working on Mr. Avella’s campaign. “We’re not sleeping any more.”Both Ms. Paladino and Mr. Avella have said the nation’s southern border should be closed because of how the migrant crisis is affecting the city.But Mr. Avella has accused Ms. Paladino of making xenophobic remarks about Asians. He sent out a campaign mailer highlighting comments that Ms. Paladino made about how many “Asian languages” there are and noting that she liked a social media post saying that the country should “stop catering to Asians” because “we speak English,” using an expletive for emphasis.Ms. Paladino said Mr. Avella had dug up “joke tweets” from years ago because he had “nothing productive to add to the conversation,” and that she had worked on behalf of Asian Americans for years.Tony Avella, left, prints campaign fliers in Mandarin and Korean, in recognition that 38 percent of his district is of Asian descent.Janice Chung for The New York TimesIn the new Asian opportunity district in southern Brooklyn, the Democratic nominee, Susan Zhuang, and the Republican nominee, Ying Tan, each held rallies in August to oppose a migrant center in Sunset Park that is not even located in their district.Ms. Zhuang and Ms. Tan have focused their campaigns on crime, quality-of-life issues and education, as they fight to represent a district that is 54 percent Asian.During a recent debate, they argued over whether the other had done enough to protect the specialized high school entrance exam and speak out against migrant shelters. Ms. Tan said the city’s right to shelter should be eliminated entirely, while Ms. Zhuang said it should not apply to recent migrants.Mr. Yang, the Democratic consultant, said that the candidates’ response to the migrant influx illustrates how many Asian American voters are more concerned with particular issues than political party lines. Asian Americans, particularly Chinese Americans, are more likely to be unaffiliated with a political party than any racial minority, he added.Hate crimes against Asian Americans is one those issues. A protest on Monday about a 13-year-old Asian teen who was beaten by an adult drew both Mr. Chow and John Liu, a center-left Democratic state senator and the first Asian American elected to citywide office.Both Mr. Liu and Mr. Chow called for criminal charges against the teen’s father to be dropped because he was acting in self-defense.“Incidents like that make people aware in terms of the importance of local elected officials,” said Yiatin Chu, president of the Asian Wave Alliance, which co-sponsored the protest. “What are they saying? How are they helping us navigate these things?”The protest was one of many recent examples of how Asian Americans are pushing elected Democrats to take their concerns more seriously.Shekar Krishnan, the first Indian American elected to the City Council, has a large Bangladeshi population in his district, but noted that there were very few Bengali dual-language programs in public schools.“Government is not hearing our concerns and not taking them seriously enough and treats us still like a monolith,” said Mr. Krishnan, who represents Jackson Heights and Elmhurst in Queens.Grace Lee, an assemblywoman who represents Lower Manhattan, and Mr. Liu are publicly working to protect the commuter vans that are prevalent in Asian communities, and make sure they are not unduly harmed by new congestion pricing rules.The vans are a form of mass transit “that is vital to the Asian American community,” Ms. Lee said. “Those are the sort of things where representation matters.”Ms. Meng said she was starting to see things change. In a recent special election in a Queens Assembly district covering Kew Gardens, College Point and Whitestone, Democrats were able to win over voters who had supported Lee Zeldin, last year’s Republican nominee for governor, instead of Gov. Kathy Hochul.The Democratic Assembly Campaign Committee ran ads in Asian media every day during early voting and worked with a Chinese newspaper to place messages in WeChat, a Chinese messaging app.Councilwoman Sandra Ung represents a district in Flushing, Queens, that has the state’s highest share of Asians.Dave Sanders for The New York TimesOn a warm Friday evening, Sandra Ung, one of the five Asian Americans elected to the Council in 2021, walked north on Main Street in Flushing to knock on doors. Asians comprise 72 percent of her district, the highest share in the city, and Ms. Ung wanted to reach older, first-generation immigrants.One woman, speaking in Mandarin, wanted help finding her polling place. Ms. Ung, a Democrat, and her campaign manager both pulled out their phones.“Ni hao,” Ms. Ung said to another woman who stuck her hand out of the door just far enough to grab a flier written in Mandarin, Korean and English. After a brief conversation in Chinese, the woman said she planned to vote for Ms. Ung.“Sometimes,” Ms. Ung said as she headed for the next apartment, “they just want to have someone who is speaking their language.” More