Open the Yandex Browser app.
Tap the three lines (≡) icon at the bottom of the screen.
Select Settings.
In the Privacy section, find and tap Clear Data.
In the list that appears, check:
Cookies
Cache
Tap Clear.
A confirmation popup will appear saying:
"Are you sure you want to clear data?"
— tap Yes to confirm.
Close the app and open it again for the changes to take effect.
How to close the app: swipe up from the bottom of the screen (or double-press the Home button), find Yandex Browser in the app switcher, and swipe it up to close.