I've my permalinks such as the following:

/%category%/%postname%

However, I remember when i published a blogpost. I later erased it, however again I added it again. It designed a permalink with "-2" behind it, or e.g.:

world wide web.myadress.com/category/publish-2

Basically alter the permalink to

world wide web.myadress.com/category/publish

It instantly changes it to

world wide web.myadress.com/category/publish-2

It is possible to way I'm able to fix this with no redirection wordpress plugin? The prior posts don't exist any longer...

Thanks ahead of time

Remove the publish in the trash. Wordpress looks towards the trash to avoid duplicate permalinks, and until that publish is erased, you're going to get the "-2" type permalinks.