Thanks, Akkana, for your excellent guide which is much better than the notes I posted previously. Having forgotten how to do it, I recently wanted to overlay a historical map in OsmAnd and followed your guide. Here are a few observations (QGIS 3.10, Windows 7):
1. I didn't have any "API Key required" problem with the QuickMapServices plugin
2. The change from QGIS 2.x to 3.x was major, and I think it broke the qtiles plugin in Linux though it still worked for me in Windows. But from QGIS 3.8 the tiles functionality is built-in:
Processing>Toolbox>Raster tools>
3. You can select .mbtiles and continue as you described, but I chose "Generate XYZ tiles (Directory) " The default settings work, but it's worth considering if you want .png or .jpg. JPG can be much smaller files without discernible deterioration, PNG can have transparent regions. OsmAnd can handle either.
4. As with the old qtiles plugin, the only remaining obstacle is that OsmAnd expects tile filenames of the form xxx.png.tile or xxx.jpg.tile rather than xxx.png or xxx.jpg as generated by QGIS. So you need to batch-rename every file in the directory hierarchy as I mentioned in an old post
https://groups.google.com/d/msg/osmand/bG1SGGNYxYI/GHvZk7wUCQAJ
Then you can just drop the directory hierarchy into OsmAnd's tiles folder.
Apart from the awkward recursive batch renaming of filenames, this way is nice because it only uses QGIS.
I offer these notes by way of thanks!