thank you for sharing your question.
I did a quick search and found 2 projects in Italy, which have been promoted to integrate the asylum seekers in the university world:
1. The project "Unibo for refugees" is promoted by the University of Bologna and the Municipality of Bologna. At the international desk, they can examine your school certificates and academic qualifications. Students have also the possibility of enrolling for single learning activities and Italian courses with exemption from fees. You can find more information here: https://www.unibo.it/en/services-and-opportunities/study-grants-and-subsidies/exemptions-and-incentives/unibo-for-refugees. You can find their contact address on the this page.
2. The second project is promoted by Politecnico di Torino. Their project operates on two areas of action: the first is dedicated to students waiting for recognition of their refugee status (asylum seekers); the second is aimed at supporting students, who already have got valid permits (refugees), in their enrolment in University and the following procedures. You can find more information here: http://international.polito.it/admission/prospective_students/re_home4students.
As asylum seeker in Italy you are not allowed to study in another country in Europe.
I hope I have answered your questions.