Hello @Miky - nice to hear from you again!
Your fingerprint and the asylum application will affect future applications for asylum. But I don’t know if your withdrawn application affects the granting of visa for EU member states or not, though.
Concerning asylum applications: You can ask for asylum in one EU-country only. That's why they take your fingerprints and add them to a database. Other countries can check back if you already applied for asylum in another country before and send you there in accordance with Dublin III convention.
Usually you can apply for asylum again (in Germany that’s called “Folgeantrag”) if there was a significant change concerning your situation since your last application or if those reasons haven’t been taken into account the last time (e.g. the occurrence of a new life threatening situation, persecution, or an illness that can’t be treated in your home country). You must do so within 3 months after your situation changed in said way.
In your case the question is now if your withdrawn application counts as an asylum application or not. Unfortunately I’m not a hundred percent sure about that, but I assume that it does count. I will link @Marcel and @Steven . They are both lawyers and share their knowledge with us on the platform. Maybe they have better insights than me.
I hope this answer was helpful to you. Feel free to ask further questions if necessary.