In a four-page opinion, Commonwealth Court President Judge Mary Hannah Leavitt dismissed the suit brought by a group of nine GOP state lawmakers, led by Rep Daryl Metcalfe, saying they had waited too long to file their challenge.
Democrats and other critics have accused Mr Trump of aiming to reduce public confidence in U.S. election integrity and undermine democracy by trying to subvert the will of the voters.
Before the court's verdict, Trump had directly appealed to the court and state officials to help him overturn the Pennsylvania election results.
Eric Schmitt, the attorney general from Missouri, announced on Twitter late Tuesday that his state is "in the fight" after Texas announced its election challenge that would invalidate the 62 Electoral College votes from four battleground states and award President Trump with a second term.
The legislators - representatives Daryl Metcalfe, Russ Diamond, Dawn Keefer, Thomas Sankey, Rob Kauffman, Stephanie Borowicz and Francis Ryan and Senator Cris Dush - claimed the vote count that shows Democrat Joe Biden winning the presidential race in Pennsylvania is "severely flawed".
Daniel Ricciardo to meet F1 bosses over Grosjean crash replays
The race is at the same circuit but on a different and shorter, "outer" layout, which Formula One has never raced before. But Daniel Ricciardo had talked about whether was a need to constantly show replays of the crash after the race.
Utah Attorney General Sean Reyes signed on Wednesday, joining the other states in a briefing in the Supreme Court. "That's because it didn't happen", Fuchs, who ran the Republican secretary of state's campaign for that job, said.
Mr Trump lost his bid for re-election last month.
"He is. Are you?" the Arizona GOP added.
The high court on Tuesday rejected, without comment, a request by Pennsylvania Republicans to reverse the state's certification of its election results.
Many of those seeking a political future in the Republican Party have been far more careful in their criticism. Georgia senator Kelly Loeffler this week repeatedly refused to acknowledge Mr Biden's win, as she hopes to persuade Trump supporters to support her in her January run-off election.
Michigan's Democratic Attorney General Dana Nessel said: "The erosion of confidence in our democratic system isn't attributable to the good people of Michigan, Wisconsin, Georgia or Pennsylvania but rather to partisan officials, like Mr Paxton, who place loyalty to a person over loyalty to their country".
In Pennsylvania, Trump's legal team wanted over 2.5 million absentee ballots to be thrown out, citing unproven claims of voter fraud.