Go to Settings → Safari (On iOS 18 and newer: Settings → Apps → Safari)
Scroll down and tap Advanced → Website Data.
Find your domain (or use search), swipe left, and tap Delete.
Restart Safari and open the site again. To restart Safari: swipe up from the bottom (or double-press the Home button), find Safari in the app switcher, swipe it away to close it, then open it again from the home screen.
Alternative: Go to Settings → Safari → Clear History and Website Data – to remove all data (cookies, history, etc.) at once.