From the feature comparison at https://github.com/meichthys/foss_note_apps only two FOSS apps support handwriting: Joplin (with a plugin) which gets a subjective 6/10 score, and TriliumNext, which gets a subjective 2/10 score. I personally dislike Joplin but many people love it, so I recommend giving it a shot.
I think TriliumNext is great, but the mobile experience is still lacking (though they are tracking several issues to improve here). There’s no dedicated mobile app but they at least have a PWA. It also needs to be self-hosted, but doing so is straightforward if you’re already using Docker. The handwriting is done via a built-in Excalidraw integration.
Here are some options not captured in that list:
Obsidian is not open source, but also has an Excalidraw plugin. I’ve not used it yet but I’ve seen multiple discussions saying that it’s very well done and has additional functionality on top of base Excalidraw. There’s also an open source (MIT) plugin for Obsidian that adds support for handwritten notes. I only use Obsidian on my work computer and haven’t used it either, though I plan to install the Excalidraw plugin Monday.
StylusLabs Write is FOSS (AGPL 3.0), multiplatform, and has a free Android apk available. Note that the Google Play version has had updates suspended. I just learned about it and don’t know how it otherwise measures up. I’m planning to check it out, though.
You can use any note app that has Excalidraw support, so long as you don’t need your handwritten text to be OCRed. That means that the following are all options:
- The Nextcloud Excalidraw integration
- Standard Notes, using https://github.com/nienow/sn-excalidraw (or if you pay for Standard Notes, official Excalidraw editor)
- The Excalidraw PWA
- A self-hosted fork of Excalidraw with Firebase replaced with something else (see https://github.com/beltebelt/excalidraw for an example)