Text messages

Unfortunately, there is no dedicated print function for Messages in iOS.

What you can do is take screenshots of the messages and print out the images from the Photo app. Alternatively, you can send the images via email to a PC/Mac connected to a printer.

You can see how to print from your iPhone here:

Use AirPrint to print from your iPhone or iPad - Apple Support

You can see how to take screenshots from your iPhone here:

Take a screenshot on your iPhone - Apple Support

You're welcome. If you use a Mac and your Apple ID that you use on your iPhone is set up on it, you can print your messages from the Mac.

Open Messages, select conversation, tap file in the top menu and select print. Alternatively, you can look for 3rd party software for PC and Mac, for example in the program iMazing you have the option to print out messages from your iPhone. However, the program is not free, but there is a trial.