In Leipzig there are several colleges/universities where Ukrainian refugees can probably study. The information on the linked pages is constantly updated. Much is still in the planning stage.
Here you can find information about the University of Leipzig. There are many courses of study at the university (University of Leipzig: Courses of Study). Here you can find information especially for Ukrainian refugees: Universität Leipzig: FAQ zum Studium. Here you can find information about German courses and enrollment for refugees: University of Leipzig: Refugees
At the Leipzig University of Music and Theatre (Hochschule und Studium | Hochschule für Musik und Theater “Felix Mendelssohn Bartholdy” Leipzigc), the Prorector is the contact person for refugees (firstname.lastname@example.org).
The Academy of Visual Arts (HGB) offers services for refugees (support for students, scientists and other people from Ukraine with and without Ukrainian passport – Academy of Visual Arts) and can be reached at email@example.com.
Information for all students in Leipzig is summarized here: Support for Students Affected by the Ukraine-Russia War | Studentenwerk Leipzig