Official Fulqrum Publishing forum - New patch on the way will it overwrite the other beta automatically?

Only the final/official patches download automatically through Steam.

For testing patches (alpha and beta versions) a link to the download is given in the forum thread that announces the patch, along with instructions. For example, "download the zip file and extract it into your main game folder, set it to allow overwrite of existing files".

These instructions depend on whether the test patch is a complete package, or an incremental one.

In the case of a complete package that is self-contained (includes all of the needed files), you can simply install over a previous version, regardless if it was a beta or an official one. In such a case, many people like to revert to the latest official version as an optional step, in order to ensure their files are not corrupted.

This is done by running "verify integrity of local cache" through Steam, which catches differences of files compared to the latest official version and restores them to that standard. In other words, you go back to the latest stable version to ensure proper file structure, then manually extract the test patch on top of that.

In the case that the testing patch is incremental (like a hotfix), it will require previous testing patches to be present because it doesn't contain everything itself. This is clearly stated in the instructions whenever it happens (for example, like the hotfix we had for the test patch recently).

In such a case, installation is sequential: you start with the latest official version and manually install/extract all subsequent test patches in the proper sequence.

This is the general layout of potential cases. Whatever happens each time, it is stated in the instructions for the patch, so you will not have a hard time deciding which is which. Cheers ;)