Template is used on blog page

I’m currently developing a wordpress theme. I’m running it locally on a apache server and I’m or at least was nearly down.
I’m using a static page as start page and and a page called blog as page for my posts. The page.php template doesn’t have a sidebar, but the index.php does. I now developed a page-template for my static home page (also without sidebar) and applied it.
Since then the template page is also applied to my blog page, which is now missing a sidebar and has some other undesired features and even if I change the home page back to the default template the blog page still displays the custom template (without sidebar).

Can anyone help?

Kind regards
zeemi