You can add this custom Publication Type in [Tridion-Install-Home]\config\Tridion.ContentManager.config in the publicationTypes section
And Restart the SDL services and IIS SDL Tridion AppPools to see the new publication type list should appear in that drop-down.
I hope it helps.
You can indeed add your own custom Publication Types. Simply edit the "publicationTypes" section of Tridion.ContentManager.config in a text editor and add your own.
As indicated by the comments in the file, you need to choose an ID that is greater than 1024 as anything below that is reserved by the system.
<publicationTypes> .... <add id="1025" name="Custom Publication Type" /> </publicationTypes>