As a Voiceover user, the Simplenote app by Automatic is an app I use daily. It's free and are versions for IOS, Android, Windows, Mac, Linux and in a browser.
Your notes sync seamlessly between platforms, no extra steps required.
You can read all about it here but I will focus on two features I find most useful as a Voiceover user of the IOS app in particular.
Markdown and preview on demand support
This app supports writing in Markdown, which is basically a user-friendly way of representing various kinds of markup like headings, lists, links, checkboxes etc.
That's not particularly unusual, lots of notes apps do have Markdown support these days. But Simplenote makes switching to a preview of your Markdown text easy. This means that if your Markdown contains headings, in the preview you can move between headings in the same way you would on a webpage. This is great, because it enables a means of scrolling effectively through long notes, which is generally not easy on IOS.
To enter the preview mode while Voiceover is running, Do a three-finger swipe to the left while the cursor is anywhere in the note. The keyboard could be showing or dismissed; it doesn’t matter. To get out of the preview, there's a back button in the top left corner.
Reading by paragraph and editing
Even without entering the preview mode, if you edit a note and then press the button in the top right corner to dismiss the keyboard, you can read by paragraph.
If you're Reading by paragraph, and find you want to edit the paragraph your cursor is on, you can double tap, and the cursor will land somewhere in that paragraph. Unfortunately, it will probably not land exactly where you would expect it to, so you do need to scroll around a bit, but it is at least an improvement on having to scroll all the way from the top or all the way from the bottom of the note.
Public links to notes
Another nifty feature is the ability to turn your note into a marked up public webpage, if you want to (notes are private by default).
To create a public link to your note using the IOS app, select a note, find and select the Menu button. Locate the Publish switch, turn it on and then copy the link.
Publishing a note in this way, especially if you’ve added headings using Markdown, makes for an easily-navigable way of presenting information. For instance, when I have written text transcripts for one-off pieces of audio, I publish them in Simplenote rather than Google Docs, because it's much nicer to read with a screen-reader or Braille and you can more easily jump between headings.
And there’s more
This was a whistle-stop tour of the features I use most. You can also collaborate on notes, link notes internally to other notes, add tags to notes and more. Here’s the IOS download link and again here is where you can read more about Simplenote.