President Trump’s re-election campaign has run menacing and misleading ads this fall accusing Joseph R. Biden Jr. of corrupt dealings with Ukraine. Republicans in Congress are scrutinizing Mr. Biden’s son, pressing the State and Treasury Departments for information about his work for a Ukrainian energy company. The president himself has unleashed a stream of unfounded accusations against the Bidens and pushed for them to appear at a potential impeachment trial in the Senate.

As Mr. Trump faces impeachment for allegedly pressuring Ukraine to investigate Mr. Biden, he and his allies are now turning those same claims about Mr. Biden and his son into a key element of their defense. And they plan to continue to hammer at the Bidens’ Ukraine dealings as impeachment proceedings move into the new year.

There is no evidence that the elder Mr. Biden, while serving as vice president, improperly intervened in Ukraine to benefit his son. But the president’s advisers are betting that many voters will ignore the complexities of the allegations and absorb a simple message about a father using his influence to help his son, a senior Trump campaign official said.

The barrage of attacks is the latest example of Mr. Trump’s monthslong fixation with Mr. Biden, who leads the Democratic field in national polling and has bested the president in head-to-head surveys in several key battleground states. Mr. Biden and many independent experts have called the allegations of corruption false, and Mr. Biden’s campaign insists that they demonstrate how worried the president is about facing him in a general election.