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There is currently no electronic record of the refusal shared between Schengen countries but such a system, the Entry/Exit System is currently being implemented. There is probably already some national record of it.
There should be a stamp in your passport that could alert border guards. Legally, it is not in and of itself a reason to refuse entry again but it could obviously invite further scrutiny.
Upvote:1
Under the terms of the EU's General Data Protection Regulation (GDPR) you have a right to know what information is held about you by any company or organisation that is in the EU. This applies even if you aren't a EU citizen or resident. However, state organisations do have the right to withhold some information for state-security reasons.
You can ask the immigration authority of the country who refused you entry, and ask for a copy of your records. There may be a charge for this; I think it is capped at €15. We have a list of how to contact EU immigration authorities, that you can use to determine the contact details.
This is a called a 'subject access request', and you should provide as much information as you can. I would recommend providing
They have to respond speedily to the request (I can't remember the timescales), thought they can reply saying the need some time to gather the information