In this article, we introduce a new geometrical structure which is the hybrid of cone metric space over Banach algebra and extended b-metric space. We prove analogues of Banach, Kannan and Reich type fixed point theorems in our introduced space. We also furnish with various concrete examples to establish the validity of our results. The obtained results generalize many well-known results in literature, especially the main results due to Vujakovic et al., Hussain et al., Huang, Radenovic, Xu become special cases of our results