Your answer is very simple:
This is the content of your .gitignore
file:
# ignore those files
.weirdBackupFileType
.travis.yml
#DONOT ignore those files (this is what the ! is for - un ignore files)
!_.weirdBackupFileType
!Z.travis.yml
And that's it.
In the image you can see that i have created the file and after adding it to the .gitignore
they are not in the status any more.