Would my fingerprints still be on file from a 2013 application?

We get a lot of questions like this and it always feels like the underlying question is "I've been rejected for visas in the past and I'd like to apply again now. If I can get away with it, lying about my past would increase my chance of getting the visa. So, if I lie, will I get caught?"

You should always assume that they know your application history, and you should answer all questions on the application form honestly and truthfully. If you are found to have lied, your application will be refused, your visa will be revoked if it has been granted, and you will be banned from applying again for some amount of time.

It sounds like you've been refused a visa more than once. You're unlikely to get a visa unless you have fixed whatever things caused the rejection of your earlier applications.

Data is kept in the VIsa Information System (VIS) used by Schengen states for five years. This retention period starts from the expiry date of the issued visa, the date a negative decision is taken or the date a decision to modify an issued visa is taken. https://ec.europa.eu/home-affairs/what-we-do/policies/borders-and-visas/visa-information-system_en