ALEXANDRA, South Africa—A quarter-century after Nelson Mandela became this nation’s first black president, his African National Congress is struggling to overcome skepticism from an unlikely part of the electorate: young black voters born into a democratic South Africa.

Heading into national elections on Wednesday, support for the ANC and its president, Cyril Ramaphosa, is lowest among the so-called born-free generation, born since Mr. Mandela became president in 1994.

High...