So I've resolved the problem by following this guide.
https://blogs.msdn.microsoft.com/adpowershell/2009/04/26/working-with-certificates-in-active-directory-powershell/
Changed the command a little bit suggested by Mathias.
Set-ADUser -Certificates
Then followed this guide to fill in the parameters of altSecurityIdentities.
https://blogs.msdn.microsoft.com/spatdsg/2010/06/18/howto-map-a-user-to-a-certificate-via-all-the-methods-available-in-the-altsecurityidentities-attribute/
Now my certificate is added to X509 Certicates in Security Identity Mapping.
Here is my code:
Set-ADUser USERNAME -Add @{'altSecurityIdentities'="X509:<I>C=BE,CN=Citizen CA,SERIALNUMBER=********<S>C=BE,CN=FIRSTNAME (Authentication),SN=LASTNAME,G=FIRSTNAME,SERIALNUMBER=***********"}
Note: you can get the X509 parameters (Issuer and Subject) by opening the certificate.
I hope this can help someone else with the same problem. And thanks again Mathias!