The name of the document which prove my studies at the university I am originally from one country but study at university in a different country. Now, my native country asked me to prove that I study at this university and I want to ask my university to bring me document for that. What is this document used to be called? 

Can I call this document "study confirmation letter" or "confirmation of studies"? 

I found (here) the phrase "proof of study" ans also "Certificate of Enrolment" (here), "proof of enrolment" (here) but "proof of study" as well as "confirmation for studies" both seems to be for those who are graduated already while I'm still student there. I would like to take you advice for the conventional way (that everybody at the university office can understand) to call what I need.
I once had to acquire a "Certificate of Matriculation" or "Confirmation of Matriculation," similar to what is described here: http://www.ed.ac.uk/student-administration/order-documents/matric-certificate.