Summary: First, we introduce the notion of \(\mathcal{MT}\)-cyclic Ćirić contractions of type \(I\) and \(II\) with respect to auxiliary function \(\varphi\). Then, we prove some best proximity point results for such mappings in the setting of metric space. Also, we will show that the fixed point is unique by additional assumption property UC. These theorems improve and generalize several results in the literature. Some examples and applications illustrate usefulness of these generalizations.