The most likely reason for the error is that the certificate authority that issued your SSL certificate is trusted on your desktop, but not on your mobile.
If you purchased the certificate from a common certification authority, it shouldn't be an issue - but if it is a less common one it is possible that your phone doesn't have it. You may need to accept it as a trusted publisher (although this is not ideal if you are pushing the site to the public as they won't be willing to do this.)
You might find looking at a list of Trusted CAs for Android helps to see if yours is there or not.
