As far as I know, SMB - the Windows File Share protocol - does not support PKI authentication directly, but does support Kerberos authentication.
So if the Windows File Share server is a member of an Active Directory domain, and you can arrange some way to use PKI authentication to get a Kerberos authentication ticket, you could use that (with the
sec=krb5i option for
mount.cifs) to mount the share. This seems to be possible, but rather complicated.
The first step would be to use
pkinit (packaged as
krb5-pkinit in some distributions) to get an initial Kerberos authentication ticket using PKI authentication. Once the user running the
mount.cifs command has a valid
krbtgt ticket for the Windows domain,
mount.cifs can automatically request a further
cifs/servername@DOMAIN.NAME ticket when
sec=krb5[i] mount option is used.
This looks like a reasonably detailed description of such a setup: