Weren’t they the kids of his maid who died unexpectedly?
Yes.
https://en.wikipedia.org/wiki/Diff'rent_Strokes
“The series stars Gary Coleman and Todd Bridges as Arnold and Willis Jackson, two African American boys from Harlem who are taken in by a rich white Park Avenue businessman and widower named Phillip Drummond (Conrad Bain) and his daughter Kimberly (Dana Plato), for whom their deceased mother previously worked.”