Will UK refusal and previous asylum record effect on EU visa

Hi, I have been in the UK with student visa. My further extension was refused due to over stayed. UK court orderd me to leave the coutry. I left UK and traveled to France to seek political asylum. Couple of months later I have voluntarily returned home country after solved my political problem. Currently I'm finishing graduation and thinking to get a master degree from an europian university. In this curcumstances am I eligble to apply student visa on any europian university? I regret for my past. Any one please give me advise or suggestion what would be the great way to get europian student visa such as any specific country who do not share those finger prints.
Many thanks for your help.