To give select students an alternative quiz/test/exam access, you will need to Manage their Special Access. To do this, click on the "Course Admin" tab in the blue navbar on the course homepage.

Then scroll down to "Quizzes" under the "Assessment" section.

Scroll to the Quiz/exam/test you want to give special access to and click the caret next to it, then click on "Edit."

On the right side of the page, click on "Availability Dates & Conditions"

Then click on "Manage Special Access"

Then click on "Add Users to Special Access"

From here you can edit start/end dates and due dates for select users. 

Click the blue "Save" button when finished.

Using the same process, you can adjust settings for timing, display, attempts, and how feedback is released to students by clicking on the options beneath "Availability and Dates."