When Michael D. Cohen needed $17 million to buy a Manhattan apartment building in 2015, he went to Signature Bank.

Signature had existed for less than two decades, and compared with some of its New York rivals, it was a small player occupying unglamorous niches.

Yet it was a natural place to go for Mr. Cohen, who was Donald J. Trump’s personal lawyer. Years earlier, he had helped initiate a relationship between Signature and Mr. Trump, and the bank became an unlikely go-to lender for the future president and his extended family.

The bank helped finance Mr. Trump’s Florida golf course. It lent money to Jared Kushner, Mr. Trump’s son-in-law, and to Mr. Kushner’s father, Charles. It provided Mr. Trump and his business with checking accounts. And Ivanka Trump sat on Signature’s board of directors while the bank was lending to her father and her husband, Mr. Kushner.

Signature provides a window into the intersecting financial interests of Mr. Cohen and the Trump and Kushner families. With Ms. Trump and Mr. Kushner working in the White House, and Mr. Cohen under criminal investigation, Signature’s interactions with some of its most famous clients are attracting attention from regulators.

New York’s Department of Financial Services this year requested information from Signature about its credit lines to the Kushners, according to people familiar with the requests. They said regulators were reviewing whether Mr. Kushner’s White House role could compromise Signature’s ability to collect on the loans.

That review of Mr. Kushner’s loan documents led the New York regulators to broaden their inquiry, said one person, who was not authorized to speak publicly about the regulator’s activities. The agency is now looking into whether Signature lent money to real estate developers — including the Kushner family’s business, Kushner Companies — knowing they planned to use abusive tactics to push out low-rent tenants and then charge more, according to two people familiar with the review. It is focused on whether Signature’s loans were overly risky and violated laws intended to prevent predatory behavior.

The inquiry is at an early stage and might include banks other than Signature, the person said.

“We recognize we are not perfect,” Signature’s chairman, Scott A. Shay, said in a statement. “However, any allegation that we knowingly or somehow actively abet tenant harassment is frankly a slander against Signature Bank and an unfair impugning of the reputations of many hardworking colleagues who strive to be a positive force for not only our shareholders and depositors but our community as well.”

Signature announced on Friday that it was stepping up efforts to make sure its lending doesn’t lead to the displacement of tenants. The pledge drew praise from the Association for Neighborhood & Housing Development, a New York community group.

Last week, Gov. Andrew M. Cuomo of New York said the state was opening an investigation into allegations, filed in a lawsuit, that Kushner Companies illegally harassed low-rent tenants to get them to leave.

Christine Taylor, a Kushner Companies spokeswoman, said, “All our business with Signature Bank has been entirely appropriate.” She added that before Mr. Kushner joined the White House, “we never had these type of inquiries which appear to be solely for political reasons.”

Amanda Miller, a Trump Organization spokeswoman, played down the company’s relationship with Signature. “While the company has, from time to time, done some business with Signature Bank, those dealings were few and far between and limited in scope,” she

said. (Other banks, such as Deutsche Bank, have done more business with the Trump Organization.)

Mr. Shay and Joseph DePaolo founded Signature in 1999 with backing from Israel’s biggest lender, Bank Hapoalim. One of Signature’s specialties was financing the purchase of taxi medallions, which authorize holders to operate cabs. Mr. Cohen had amassed a large portfolio of medallions and had borrowed money from bankers who later joined Signature.

Signature forged deep political connections — its board members have included a former Republican senator, Alfonse D’Amato, and a former New York lieutenant governor, Alfred B. DelBello, a Democrat. A former Democratic congressman, Barney Frank, joined the board in 2015.

The bank also became known for doing more than rivals to accommodate customers.

For example, Signature allowed some business clients to withdraw cash even when their accounts were empty, creating overdrafts of tens of thousands of dollars without formal loan agreements, according to a former employee and a client who said he routinely did this. That attracted clients with irregular cash flow.

In an interview at Signature’s Fifth Avenue headquarters, Mr. DePaolo, the bank’s chief executive, acknowledged that Signature did things that rivals wouldn’t. He said it was part of providing superior services to trustworthy customers. He and Mr. Shay said Signature complied with all banking rules.

Mr. Frank said Signature served a valuable role by financing housing for low- and middle-income tenants. “It’s very well run,” he said.

Before Mr. Trump became a Signature client, he fought the bank. The 2007 skirmish involved a construction company that Mr. Trump had hired to help build a golf course. After Mr. Trump refused to pay the company’s bills and sued it for subpar work, the company went bankrupt. It owed Signature money. Mr. Trump’s and Signature’s lawyers argued in court that their clients were both entitled to the same funds from the bankrupt company.

Mr. Trump and Signature settled in September 2009. Three months later, the Trump Organization started borrowing from Signature — thanks, at least in part, to Mr. Cohen.

Mr. Cohen had joined the Trump Organization in 2007 as an executive and was on the condominium board of Trump World Tower, across from the United Nations. In December 2009, Signature lent $800,000 to the building, managed by the Trump Organization, to refinance the mortgage on the superintendent’s apartment.

A former Signature employee said Mr. Cohen had helped arrange the loan. Signature executives say they have no record of Mr. Cohen’s involvement.

A long-term relationship between Signature and the Trump family ensued.

In 2010, the year after Ivanka Trump and Jared Kushner married, Charles Kushner and his wife opened a Signature account, a bank spokeswoman said. That year, the Trump International Golf Club in Florida received two letters of credit from Signature totaling $212,000. The letters provided a guarantee from Signature that Mr. Trump would be able to pay what he owed in a contract with a third party. Signature said the letters of credit were fully secured by cash that Mr. Trump had at the bank.

Signature in 2011 gave Charles and Jared Kushner a credit line from which they borrowed nearly $5 million that year, securities filings show.

In September 2011, Signature named Ms. Trump, who was 29, to its board. She was paid $198,875 in 2012 in cash and stock.

Mr. Shay said Ms. Trump had been invited onto the nine-member board as part of an effort to recruit younger directors and to give it a second woman.

“She was an active, engaged board member,” Mr. Shay said. “She read everything and asked questions if she didn’t understand.”

Giving seats on the board of a publicly traded company like Signature to people directly connected to large clients is generally frowned on.

“Directors should not have significant commercial relationships with institutions on whose boards they sit,” said Charles Elson, a professor of corporate governance at the University of Delaware. “You’re there to oversee operations and be objective. Your job is not to guarantee business for the bank or the company but to ensure effective oversight.”

Signature nonetheless designated Ms. Trump as an independent director and assigned her to board committees that set executive compensation and monitored risks.

The bank continued to do business with her family. It renewed credit lines to the Kushners, who by the end of 2012 owed the bank $4 million.

Mr. Shay said that Ms. Trump had recused herself from decisions involving her family and that the transactions hadn’t been large enough to compromise her independence.

With the benefit of hindsight, Mr. DePaolo said, “I almost regret that we had Ivanka on the board.” Mr. Shay added: “Had we known the identity of the 45th president, I think we would have thought twice. But that’s not to say she wasn’t a great board member.”

Ms. Trump stepped down from the board in early 2013 because of “her highly demanding schedule.” A White House spokesman didn’t respond to requests for comment about Ms. Trump’s role.

Five months later, Signature started making mortgage loans to Mr. Kushner’s company. Kushner Companies has received at least 21 mortgages from Signature, totaling more than $210 million. The loans were mostly for buildings in Manhattan and Brooklyn where many tenants live in rent-regulated apartments.

“All the lending we’ve done with them has been very conservative,” Mr. Shay said.

In February 2015, shortly before Mr. Trump’s presidential campaign got underway, Signature made the $17 million loan to Mr. Cohen.

Mr. Cohen said in an email that the loan had been “sourced by a mortgage broker and not based upon any personal relationships.”

Mr. DePaolo said that at the time of the loan, Mr. Cohen wasn’t a public figure. “We did a background check, and nothing out of the ordinary came up — he looked fine,” he said.

Signature has kept lending to the Kushners. Last year, Mr. Kushner and his father took advantage of the latest in a series of credit lines provided by the bank, borrowing more than $5 million, according to Mr. Kushner’s most recent government ethics filing.

Signature executives argue they are being punished unfairly for lending that mostly took place before the election.

“We feel abused,” Mr. Shay said.

A correction was made on 

July 23, 2018: 

An earlier version of this article mischaracterized the nature of the financial backing that Signature Bank provided to Donald J. Trump’s Florida golf course. Although the bank itself categorized the financing as a loan, it was in the form of letters of credit. Signature did not loan money to the golf course.