The story traces back to 2018, when he told the anecdote while recounting his decision to join presidential nominee Barack Obama as his running mate.

https://www.snopes.com/fact-check/howard-stern-biden-interview-desegregation/

Biden Was Arrested as a Kid While Standing with Black Family as People Protested Desegregation?

U.S. President Joe Biden was arrested as a kid while standing on a porch with a Black family as people protested segregation.

^{Nikki Dobrin (Snopes.com)}