Letters, notes, prescriptions, etc look professional and more official once they are printed on letterhead paper bearing with your signature at the bottom.

When you are on the go, and you don't have access to a laptop or desktop you can use a PDF letterhead stored in your iPhone, following the steps below. (The process has been tested on an iPhone XS Max running iOS 13.7.)

You can use a pdf letterhead you already have that's any paper size like Letter, Legal or A4, A5, etc. If your letterhead is in another file format, use the software you created it with to export it to pdf.

I'm going to use as an example one which I'm attaching here in case you'd like to experiment. Its size is A5 (half A4).

You can download the example file here

Send it to your phone using Airdrop, iMessage, or any other App of your choice or directly download it to your files.
Save the file in your Files folder (locally on your device or in iCloud) in a folder that you can easily access.
Pull up the file and click on the little pen nib icon in the upper right corner.

That will bring up a choice of writing instruments at the bottom of the screen, including an eraser. You can use any one of the choices, to write, draw, and you can also add shapes, Text, a signature, or a magnifier by tapping on the + icon in the bottom right corner. (a drawback of the text tool is that the text is middle aligned)

Once you're done editing, you can hit "Done" in the upper left corner. You can then share the saved file with anyone using any of your favorite apps.

To delete the content of the letterhead and re-use for another purpose you have two options:

Just pull it up from your files, use the eraser (pixel and object) to delete the content, and hit done. Your file is saved to its original form and ready to be re-used.
Pull up the pdf from your files, tap on the plus sign at the bottom and draw a white rectangle over any previous text, and hit done.