There is no enrolment filter for the global search. Two possible workarounds are:
1) Add the name of the enrolment method to the course summary, which is included in the global search "Courses" filter.
2) Create a course custom field for this.
Call it something like "enrolment method" and then fill it out with the text you need, eg. manual, self, etc. (You can set these in bulk using the course upload tool to save a lot of time, see the documentation on this. Then that text will be available in global search by choosing the "Course custom fields" filter. (Be sure to enable that in Plugins > Search > Search areas.) Such custom fields also appear beneath the course summary when you are using the Course list on the front page, too.
