Check this solution. it is for sharepoint 2010 but should work also for sp2013
SharePoint 2010 Permission Report: Check Access Rights for a Specific User
Refer to below given informative resources that might helps you to get this job done:
SharePoint 2013 Permission Report: Find Access Rights for Specific User in Farm
https://gallery.technet.microsoft.com/office/SharePoint-Permission-2840f327
SharePoint 2013 PowerShell: How to get user permissions report
Powershell Script to Find Specific user Permission for a SharePoint Site:
http://www.c-sharpcorner.com/code/485/powershell-script-to-find-specific-user-permission-for-a-sha.aspx
SharePoint: Get list of all users which have permissions on a sharePoint using PowerShell script
http://mstechtalk.com/sharepoint-get-list-users-using-powershell-script/
You may also take help from below given earlier discussed threads:
Powershell script to get user permission on site collections and subsites
List of all users with permission of site and various subsite
User Information List in SharePoint All details:
https://gallery.technet.microsoft.com/office/User-Information-List-in-8b420e8c
source: https://social.technet.microsoft.com/Forums/ie/en-US/ea6a1646-9b29-4598-8a88-af6bb0f72c9d/powershell-script-to-check-all-permissions-for-a-particular-user-in-a-site-collection?forum=sharepointadmin
Here is quite detail analyzing steps: How to Determine Where a User Has Been Granted Access in SharePoint
The PowerShell script: Report Where and How SharePoint Users Have Been Granted Access
Here are something else related:
https://sharepoint.stackexchange.com/questions/136581/how-to-check-one-users-permissions-for-all-sites-subsites-in-a-site-collection
https://sharepoint.stackexchange.com/questions/81100/powershell-script-to-find-permissions-for-a-specific-user
SharePoint 2010 Permission Report: Check Access Rights for a Specific User
SharePoint: User Permissions detail report for a Web Application
https://gallery.technet.microsoft.com/SharePoint-Access-Report-ac5e8235
http://nikcharlebois.com/get-a-list-of-sharepoint-permissions-for-a-user-using-powershell/