The main purpose of this research is to establish a new generalized ${\xi }^{\ast }$-Kannan type double controlled contraction on a sequence and obtain fixed point results for a pair of multivalued mappings in left $K$-sequentially complete double controlled dislocated quasi metric type spaces. New results in different setting of generalized metric spaces and ordered spaces and also new results for graphic contractions can be obtained as corollaries of our results. An example is presented to show the novelty of results. In this paper, we unify and extend some recent results in the existing literature.