Yes, some banks offer debit or prepaid cards for younger users or teenagers, but the minimum age, limits, and permissions vary depending on the product.
Check purchase and withdrawal limits, online and international usage, and whether parental controls are available.
The goal is to provide a card that suits the user's age, not simply give them a copy of an adult's card.
The figures, fees and limits in this answer vary by bank and change over time — confirm them with your bank or the official source before acting.