Emails released by the State Department over the past 18 months show that Huma Abedin frequently handled classified information — suggesting a major reason why the FBI has been eager to get a full look at the personal computer she shared with her now-estranged husband.

That computer has become the center of a major political flap in the final week before Election Day. Ms. Abedin’s boss, former Secretary of State Hillary Clinton, is trying to fend off concerns that there is a smoking gun still to be found among her top personal aide’s messages.

But the track record indicates a reason for concern: Of the messages Mrs. Clinton turned over to the State Department, nearly 5,000 were sent to, or received from, Ms. Abedin. More than 180 of those contain information now determined to be “confidential,” and one message is deemed to contain “secret” information.

In the “secret” message, Ms. Abedin forwards to Mrs. Clinton information about a 2009 ballistic missile test by North Korea.

“It is frankly remarkable that the FBI and Justice Department are only now investigating Abedin’s connection to Clinton’s mishandling of classified information,” said Tom Fitton, president of the watchdog group Judicial Watch, which has sued to try to get to the bottom of the Clinton-Abedin connection at the State Department.

The FBI has renewed its probe into Mrs. Clinton’s handling of classified emails based on what it might find on Ms. Abedin’s computer, obtained in a separate investigation into Ms. Abedin’s estranged husband, former Rep. Anthony D. Weiner.

The Weiner investigation is the latest involving the Clintons and those in their circle. It joins a reported investigation earlier this year into the Clinton Foundation; another into campaign donations to Virginia Gov. Terry McAuliffe, a longtime fundraiser and political ally; and the renewed look at Mrs. Clinton’s handling of classified information.

Whether anything on the Abedin-Weiner computer is relevant to the investigation into Mrs. Clinton, which the FBI closed in July, is heatedly debated.

Mrs. Clinton’s team insists there is nothing to be found, and they have excoriated FBI Director James B. Comey for publicly announcing less than two weeks before an election that he is looking at the new emails.

Ms. Abedin’s attorneys say the longtime Clinton aide — who is virtually guaranteed to get an influential White House post if Mrs. Clinton defeats Republican Donald Trump on Election Day — was wholly unaware that any of her messages were on Mr. Weiner’s computer.

“From the beginning, Ms. Abedin has complied fully and voluntarily with State Department and law enforcement requests, including sitting for hours-long interviews and providing her work-related and potentially work-related documents,” her attorney, Karen Dunn, said in a statement Monday night. “She only learned for the first time on Friday, from press reports, of the possibility that a laptop belonging to Mr. Weiner could contain emails of hers.”

She said Ms. Abedin will be “forthcoming and cooperative” with the latest FBI investigation, which surely will drag past the election.

Mrs. Clinton briefly addressed the controversy on Monday by acknowledging that voters had questions about the FBI inquiry, But during an appearance in the battleground state of Florida on Tuesday, Mrs. Clinton dropped all references to the investigation and instead slammed Mr. Trump’s past statements about women.

“Some of what we’ve learned, some of this stuff is very upsetting,” she said before reciting some of Mr. Trump’s most inflammatory comments.

Mr. Trump and fellow Republicans, meanwhile, have tried to keep attention focused on the FBI’s renewed probe, saying it shows voters what to expect if Mrs. Clinton wins the White House.

Indeed, the Clinton family and its allies have faced an extraordinary number of investigations over their quarter-century in Washington.

“There’s an interesting circumstantial case to be made how much smoke there has been surrounding the Clintons over the years,” said Chris Jenks, a law professor at Southern Methodist University and a former attorney adviser at the State Department.

In addition to the investigation of Mr. Weiner, whose sex-related text messages may have been sent to a juvenile, the FBI also reportedly pushed this year to open public corruption probes of the Clinton Foundation, citing concern about rewarding donors with special political access and favors.

The Justice Department, which last year found insufficient evidence to open a case, declined to investigate, CNN reported.

“We are not aware of any investigation into the Foundation by the Department of Justice, Federal Bureau of Investigation, or any United States Attorney’s Office and we have not received a subpoena from any of those agencies,” the Clinton Foundation said in a statement.

But the difference of opinion between FBI agents and Justice Department prosecutors roiled investigators, according to The Wall Street Journal, which this week reported that agents from the FBI’s New York field office continued to pursue a case until at least as recently as August. That month, a senior Justice Department official called Andrew McCabe, the bureau’s second in command, “to voice his displeasure at finding that New York FBI agents were still openly pursuing the Clinton Foundation probe during the election season,” The Journal reports.

News also leaked this year that the FBI was investigating Mr. McAuliffe, who in addition to being a political ally also served as a board member of the Clinton Global Initiative, an endeavor of the family’s charitable foundation.

News reports from May indicated that the investigation involved $120,000 worth of donations made to Mr. McAuliffe’s 2013 campaign by Chinese businessman Wang Wenliang. Mr. Wang’s companies also donated $1 million to $5 million to the Clinton Foundation, and investigators were reportedly probing the legality of the campaign contributions.

When news of the probe leaked in May, Mr. McAuliffe said he had “no personal relationship” with Mr. Wang and that a team of lawyers vetted his campaign donations, finding that Mr. Wang had held a green card since 2007, making him eligible to donate.

The Washington Post reported this week that federal investigators have also been looking into Mr. McAuliffe’s time on the board of the foundation.

Analysts say the sheer number of investigations surrounding Mrs. Clinton will raise questions in the minds of voters. Because those investigations are likely to continue into next year, they could dog Mrs. Clinton if she wins the White House.

Rep. Jason Chaffetz, Utah Republican and chairman of the House Oversight and Government Reform Committee, has already said there is plenty of room for investigations.

Mr. Jenks, the SMU professor, said that could immediately strain relations between Congress and Mrs. Clinton and her staff.

“It’s going to be painful,” he said.

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