HARRISBURG — As Pennsylvania’s vote count Friday put Joe Biden ever closer to capturing the presidency, state Republicans increasingly shifted their attacks in and out of court toward the woman who oversaw the process, even while acknowledging they had no evidence of widespread voter fraud.

State Senate Majority Leader Jake Corman (R., Centre) accused Secretary of State Kathy Boockvar — Pennsylvania’s top elections official, and an appointee of Democratic Gov. Tom Wolf — of giving faulty guidance and making unlawful changes to election rules that had undermined confidence in Pennsylvania’s results.

Boockvar, he said, had overseen a chaotic and faulty process that had sowed doubt about the vote. Corman criticized her for permitting counties to count votes that arrived late — though postmarked before 8 p.m. on Election Day — and allowing local election boards to alert voters who had submitted their mail ballots with clerical mistakes.

“Let me be very clear: I have no knowledge of any voter fraud. I have no knowledge of any misdeed, other than the process,” Corman told reporters at a news conference alongside House Speaker Bryan Cutler (R., Lancaster). “Unfortunately, the actions of the Department of State have brought that into question.”

Republicans won one legal victory of sorts late Friday when U.S. Supreme Court Justice Samuel Alito, in response to a GOP request, ordered all Pennsylvania counties to segregate late-arriving mail ballots from the rest and keep separate tallies in case the high court decides to revisit whether they should be included in the final results.

Meanwhile, a Pennsylvania Commonwealth Court judge in Harrisburg denied a bid by Republican lawyers to block counties from counting potentially hundreds of votes across the state. The votes in question were cast in person on Election Day by people who been alerted that they had made errors in their earlier mail ballots.

All of it came as the reelection chances of their candidate, President Donald Trump, dwindled with each new batch of counted ballots, prompting Trump to turn to Twitter and vow his legal fusillade was ""just now beginning!"

“I had such a big lead in all of these states late into election night, only to see the leads miraculously disappear as the days went by,” he wrote. “Perhaps these leads will return as our legal proceedings move forward!”

Democrats likened Trump to a football coach who wanted the game halted merely because his team had scored early. They said there was no mystery to the disappearance of Trump’s lead since Tuesday night — that it reflected the delayed counting of mailing ballots that skewed heavily Democratic after Trump had discouraged that kind of voting.

Boockvar, a once obscure official plunged into a moment of media stardom, has defended her advice and fought back in court against each new allegation. She has rebuffed Republican calls for her resignation that began within hours of polls closing on Election Day. Cutler on Friday demanded Wolf launch an audit of the election.

But Wolf has called the GOP’s broadsides merely partisan and said he will support her and other election officials as they work to finish counting votes.

“Attacks like this are an attempt to undermine confidence in the results of the election, and we should all denounce them for the undemocratic actions they are,” the governor said.

As in other battleground states, like Georgia and Nevada, the increasingly focused Republican legal campaign in Pennsylvania has so far appeared aimed less at disqualifying large swaths of votes than at kicking up enough dust about the process to cloud perceptions of the election’s integrity.

Boockvar, Wolf and other Democrats have faulted Republicans in the legislature for failing to pass legislation that would have allowed counties to start processing the more than 3 million mail ballots before Election Day. Counties had pleaded for the extra time, which would have allowed them to have a total vote count by election night or soon after.

As of Friday evening, counties had counted 2.5 million mail ballots. With another 100,000 left to tally, as well as provisional ballots, Biden was leading Trump by more than 20,000 votes, according to returns on the Department of State’s website.

And as the count stretched into a fourth night, Pennsylvania Republicans hoped that the close margin would hold so victories in court might still tip the balance.

Alito’s ruling came after Republicans, for the third time, urged the U.S. Supreme Court to overturn the three-day grace period for late-arriving mail ballots and sought a court order that none of those votes be added to the count. The extension had been authorized by Pennsylvania’s highest court in mid-September in a ruling that allowed counties to count ballots received up until 5 p.m. Friday — as long as they had been postmarked by Election Day.

Boockvar had already advised counties to segregate, but still count, any mail ballots that came in after Nov. 3 because it was uncertain whether they would be included in the final tally.

In their brief Friday, the state GOP argued it was unclear whether counties were consistently following her instructions.

Alito’s late-night response threw the power of a court order behind those previously advisory guidelines — and signaled that the U.S. Supreme Court may have inched one step closer to taking up the dispute. Alito, an appointee of George W. Bush, fielded the GOP response as the justice assigned to handle such matters from Pennsylvania and adjacent states.

State election officials have not responded to repeated requests for information on how many late-arriving ballots counties have received. But Boockvar and others have said that the number is small — in the hundreds in some counties

In a separate case before the Commonwealth Court, Republicans attacked Boockvar for advising counties they could share information with political parties about mail ballots that arrived with deficiencies, like missing signatures, dates, or secrecy envelopes, that could disqualify them.

That allowed parties, or in some cases county elections officials, to warn voters in time to correct those mistakes or cast a provisional ballot in-person on Election Day.

Republican lawyers argued the state’s election code doesn’t allow that. In a five-paragraph order Friday, Commonwealth Court Judge P. Kevin Brobson did not address that question of legality, ordering only that counties keep “segregate and secure” any provisional votes cast at the polls by voters who had earlier sent in defective mail ballots.

Still, lawyers for Republicans emerged from court portraying the ruling as a win — a refrain echoing among their counterparts nationally.

Around the time the order came down, U.S. Sen. Ted Cruz (R., Texas) tweeted: “When you’re breaking the law, ignoring court orders, counting ballots in secret & threatening to steal the presidency, it’s not ‘PA’s business. It’s America’s business.’”

His jab drew a quick response from Pennsylvania Attorney General Josh Shapiro, whose office represented Boockvar in the case.

“Counselor, as you may recall from your days practicing law, in court we deal with facts and evidence — you have none,” wrote the newly reelected Shapiro. “Plus, the Dallas Cowboys suck. Case closed.”