Thumb file locations

I wish to display the thumb of an image from another folder. At the moment wordpress display the thumb/medium etc… from the location of the original e.g.
/2013/06/picture.jpg
picture-150×150.jpg {it assumes the thumb is in the same folder}

How can I get it so it doesn’t assume it is in the same folder? In _wp_attachment_metadata, I tried to specify the thumb folder e.g. /thumbpics/picture.jpg, but all it does is https://www.example.com/2013/06/thumbpics/picture.jpg, but it should be in https://www.example.com/thumbpics/picture.jpg