If you want your certificate to be valid for both *.mysubdomain.example.com and mysubdomain.example.com , it must have the name of an alternative object name.
The *.mysubdomain.example.com does not cover mysubdomain.example.com .
These rules are defined in RFC 2818 and refined in RFC 6125 :
If the wildcard character is the only character of the left-most label in the presented identifier, the client SHOULD NOT compare against anything but the left-most label of the reference identifier (eg, *.example.com would match foo.example.com but not bar.foo.example.com or example.com).
In practice, this is really the way most browsers react.
However, it is likely that the CA issuing the substitution certificate for *.mysubdomain.example.com will also add the SAN for mysubdomain.example.com . Contact your CA.
Bruno
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