Dawid is correct and this is not available out of the box. The search box applies all the indexes that are set in the settings. As the search index is considered to be a back and part and the user usually does not know what does the index contain.
For example you can use two web parts on the site with different indexes and enable only one of them in the codebehind where the code would pass information what index had been chosen. Or you can set the index that you want to use directly in the code of the web part with use of the query param.