A student can attempt a quiz once per assignment. If a quiz is assigned more than once, a student will be able to take the quiz each time it is assigned.
If you wish to assign the test again to a certain number of students, you must first assign the test to the class and then remove all the students except those that you wish to retest.
A common case of multiple quiz assignment is a pre- and post-test. If a teacher assigns the quiz as a pre-test, the student can take the quiz then. Then, a few weeks later, the teacher re-assigns the quiz to measure growth. The student will be able to take the quiz again.
Then, the teacher and student will be able to compare the quiz scores, as each will be recorded.