There haven't been any formal accusations, complaints, arrests, or investigations that implicate Joe Biden in any sort of sex crimes involving kids.
Allegations of child abuse are a prominent part of the QAnon conspiracy theory, which alleges that a cabal of Satan-worshipping pedophiles runs a global child sex-trafficking ring that has been plotting against U.S. President Donald Trump. Both Trump and his son, Donald Trump Jr, have accused Biden of pedophilia on Twitter. Trump Jr. later claimed he was "just joking" in a Twitter post, yet also repeated the insinuation by saying Biden should stop his "unwanted touching" and posted a collage of Biden photographs with children at White House events.
While some adult women have accused Biden of unwanted touching in public, and former Senate staffer Tara Reade accused him of sexual assault, there have never been any credible accusations of Biden engaging in inappropriate conduct with children.
The Biden campaign denied the allegations made by Reade and an investigation conducted by the New York Times stated, "No other allegation about sexual assault surfaced in the course of reporting, nor did any former Biden staff members corroborate any details of Ms. Reade’s allegation. The Times found no pattern of sexual misconduct by Mr. Biden."
Similar exercises were carried out by the Associated Press and PBS Newshour based on extensive interviews with former Biden staffers who also asserted that they never heard of or experienced sexual harassment, assault, or misconduct by Biden. David Axelrod, a former top aide for President Barack Obama's 2008 campaign, stated that the vetting process for choosing Biden as the Vice President did not find any allegations of sexual misconduct. The veracity of Reade's allegations was also doubted due to the timing of her allegations and the changes in her version of the story. Reade is under criminal investigation by prosecutors for allegedly lying under oath about her educational credentials in her appearances as an expert witness on domestic abuse.
On social media, the accusations of Biden being a pedophile are often accompanied by images, memes, GIFs, and videos of Biden, many of which are used out of context. In one of the photos, Biden is leaning down by a boy with his hand cupped on the child’s face. The child is his grandson and the photograph was taken at the funeral of Beau Biden, Biden’s son who died of cancer. Another image that has been circulated frequently is also from the funeral where Biden is seen kissing the top of his granddaughter’s head as she stands holding her mother’s hand. These pictures are shared without any context along with unsubstantiated claims.
Furthermore, the parents of the children have spoken out against claims that Biden behaved inappropriately around their children. One often-used photo shows Biden touching a young girl’s arm. He leans in to whisper something as she looks slightly uncomfortable. The image is of Maggie Coons, Sen. Chris Coons of Delaware's daughter, during her father’s swearing-in ceremony in January 2015. After the clip went viral, Sen. Coons, a Democrat, told Fox News host Chris Wallace that Biden was simply offering her reassurance and that his daughter didn’t think Biden was being creepy. "I could hear him," Coons said in the interview. "He was leaning forward and whispering some encouragement to her about how, when he was sworn in, his daughter Ashley was 13, and she felt awkward and uncomfortable."