Messages

If it is a bubble looking shape then that is called pinning. You must have pinned your favorite conversation to the top. Press and hold the bubble/conversation and select unpin.

This happens on iOS 14 or higher

iOS 14 introduced Message 'pinning'. It's possible that you pinned it?

from the list of messages, you can pin a message by swiping right on the message thread.

Once pinned it parks up top. To edit those pins, press and hold one of the pinned messages and a menu should pop up with a preview of the conversation and some options at the bottom. You can select 'Unpin'

Alternatively when looking at your list of Message threads you can tap the 3 dots in the upper right, in the menu that opens select 'Edit Pins'. This will show yellow pins to the right of all the threads, you can select and pin those.

Up top you should see existing pins with a little minus sign to remove. tap the minus sign.