Refusal on these grounds...
One or more member state(s) consider you to be a threat to public
policy, internal security, public health as defined in Article 2(19)
of Regulation (EC) No 562/2006 (Schengen Borders Code) or the
international relations of one or more of the member states).
...means you will require a law practitioner with a specialty in EU law. It is a waste of time to solicit advice from the internet because the answers will fall into one of four categories...
- Get a lawyer
- Do something stupid (forged passport or covert entry)
- Rants from jingos telling you and your kind to stay where you are
- Incoherent drivel from random morons
People who have become listed as threats to the zone's security have backstories that require lengthy discourse with a specialist and there are no other viable alternatives. The same rationale goes for questions about appealing the decision. Attempting an appeal on this reason is perilous and moreover risks having all your stuff entered into the public domain! See a qualified practitioner!
The practitioner is needed even if the time window for an appeal has elapsed. There are data protection laws and freedom of information laws that require local expertise to navigate successfully. "Clearing your name" is not a simple job.
Related answer: Schengen Visa Refusal: Justification for the purpose and conditions of the intended stay was not reliable
NOTE: In order to preempt the natural corollary, let's add that...
- The consulate has already told the Department of Homeland Security in
the USA that you are trying to mobilize;
- The consulate has already told the other Schengen members about it;
- The consulate has informed its colonial missions abroad; and
- The consulate has informed the UK that you are attempting to mobilize
and the UK has in turn informed the Republic of Ireland and the
Commonwealth members to put a stop flag on your passport.
Update 21 April 2016
Questions from phoog (to whom thanks) about the possibility of this refusal arising from mistaken identity prompted an exchange of email with a specialist. The result being that this reason ("One or more member state(s) consider you to be a threat to public policy...") means they got a biometrics hit or some other conclusively positive match. It's not like the American no-fly list where people with the same names generate confusion. Instead it means that person (and nobody else) is in trouble and it's not going to get fixed in the near term. Hence the above answer still applies. I am taking the advanced law course in Schengen this summer and may add another update to this answer after that.
Also note that if they cannot get a positive, verifiable match they will not use this reason; instead they will use Schengen Visa Refusal: Justification for the purpose and conditions of the intended stay was not reliable
Related article on requesting your transcript from the Schengen Information System: How can I find out if someone is in the Schengen Information System (SIS)? Note: even if you find erroneous information in your transcript, you'll still need a skillful practitioner to get it officially removed and restored to its original state.