Congressional Republicans issued subpoenas to the president’s son, Hunter, his brother James, and Biden family associate Rob Walker.
So far, the Republicans' year-long investigation has failed to implicate Mr Biden in any wrongdoing.
The White House has dismissed the investigation as a political ploy aimed at hurting Mr Biden, a Democrat.
They say the probe is a blatant attempt to help former President Donald Trump, the early front-runner for the 2024 GOP presidential nomination, as he runs again for the presidency.
Republicans opened their impeachment inquiry in September, alleging evidence of President Biden's role in his family members' domestic and foreign business dealings.
But at the Oversight Committee's first hearing, no concrete evidence was produced that Mr Biden had committed any impeachable offences.
In a statement on the latest step, committee chairman James Comer, of Kentucky, said: “The House Oversight Committee has followed the money and built a record of evidence revealing how Joe Biden knew, was involved, and benefited from his family's influence peddling schemes.
"Now, the House Oversight Committee is going to bring in members of the Biden family and their associates to question them on this record of evidence.”
Hunter Biden was ordered to testify under oath before the committee on December 13 while James Biden and Mr Walker were asked to appear on 6 December and 29 November respectively.
The Republicans have also requested that James Biden's wife, Sara Biden, and Hallie Biden, the wife of the president's deceased son Beau, appear voluntarily for transcribed interviews.
Democrats have hit out at the “vengeful” orders to give evidence.
Hunter Biden's attorney Abbe Lowell called the subpoenas “yet another political stunt" and said the investigation has been full of “worn-out, false, baseless, or debunked claims."
“Nevertheless, Hunter is eager to have the opportunity, in a public forum and at the right time, to discuss these matters with the Committee," he added.
The impeachment inquiry slowed down in early October after Kevin McCarthy was ousted as speaker by a handful of fellow Republicans, before Mike Johnson was elected in his place late last month.