The EU has some confusingly-written information about your rights to access data about you which is stored in the SIS:
If data about a person are stored, that person has the right to request access to those data and make sure that they are accurate and lawfully entered. If this is not the case, the person has the right to request correction or deletion.
And how to make such a request:
If you believe your personal information has been misused, needs to be corrected or deleted, you can request access to and rectification of your data. If you are a third-country national you can address your request to the consulate of any Member State. If you are a citizen of a Member State you can either address your request directly to the competent national authority responsible for the issuance of the alert or indirectly to the national Data Protection Authority.
Guidelines on the national procedures for access requests have been compiled by the national Data Protection Authorities.
If you are an EU citizen or resident, you are probably best off referring to the relevant authorities in your country. If you are lucky, they will provide clear instructions for doing so. For example, the Norwegian police have a page (in English) called “Do you want to access the Schengen Information System (SIS)?” which contains a form to fill out, an address to mail the form to, and instructions for proving your identity. They also describe the types of information you might be able to find in the SIS:
The SIS database may contain information about:
- Individuals who are the subject of an arrest warrant or extradition request.
- Individuals who are wanted by the authorities for some other reason.
- Individuals who are not entitled to enter or stay in the Schengen area.
- Individuals who have been reported missing.
- Lost or stolen items, such as motor vehicles, vehicle registration plates or identity documents.
According to the EU page above, if you are not in Europe, you are supposed to direct your request to the embassy or consulate of any member state. I imagine that most consulates receive relatively few such requests, though, so you might want to email in advance to see what kinds of information they will require in order to process your request, or possibly you may be advised just to contact the relevant national authorities directly.