「大学付属」は
affiliated with 〇〇 university
connected to/with 〇〇 university
を使って表現します。
例:
My daughter goes to a preschool that is affiliated with 〇〇 university, but we're not sure if we're going to put her in the elementary school that is also connected to the same university.
「娘は〇〇大学の付属幼稚園に通っていますが、同じ大学の付属の小学校に行かせるかまだ悩んでいます。」
ご参考まで!