Ashley’s younger brother in The Fresh Prince of Bel-Air is Nicky Banks. He is the youngest child of Philip and Vivian Banks and is introduced late in season 3, not season 4—a timing detail that is often misremembered because the character remains prominent afterward.
Nicky’s arrival follows Vivian’s pregnancy storyline and expands the Banks household beyond Hilary, Carlton, and Ashley. Because he first appears as a newborn, several infants portrayed him during his earliest appearances. Ross Bagley later became the familiar child actor associated with Nicky when the character was older and more visible in the series.
The season reference in the question is slightly off, but “Nicky” remains the canonical answer to Ashley’s younger brother. His full name is Nicholas “Nicky” Banks, and he is Will’s younger cousin. The character is also sometimes confused with Will’s relatives or with Ashley’s older brothers, but Nicky is the baby brother added to the Banks family during the show’s third season.