e-Card Berries .

For Pokémon Ruby and Sapphire, the paired games had an exclusive feature that allowed them to scan e-Reader Cards and obtain a special berry.
Pokémon holding these berries were not allowed to be traded to other main series games.
Pokémon holding these berries were also not allowed to be traded to Colosseum or XD, nor transferred to Pokémon Box: Ruby and Sapphire.

Once you scanned the e-reader card (or injected the berry card data), you can collect the berry from Norman in Petalburg City Gym.

Pokémon holding these berries were allowed to be Pal Parked into Generation IV, however their held item would become the Enigma Berry.
In Generation III, there is no legitimate way to acquire the Enigma Berry, as it is merely a placeholder in those games.

Additionally, the data for these e-Card Berries do not exist in the ROM data of the Gen III games;
the e-Card data is loaded into the save, and the game uses the placeholder Enigma Berry to display the stored data.
So in reality, the player is merely holding onto the Enigma Berry, but the player would not know, as the data shown belongs to the e-card Berry scanned.

These e-Card berries can be injected using @suloku's tool.