This was often or usually in the form of private Christian schools formed for the explicit or implicit purpose of keeping white children out of schools with black children.
I attended one such "segregation academy" in Gadsden, Alabama in the 1970s.
Today, it's still very common to see conservative Christian schools with almost no Black children in attendance. And as a special bonus, such schools usually also discriminate against LGBTQ children and children with LGBTQ people in their immediate families.