DNA sequencing techniques are critical in order to investigate genes' functions. Obtaining fast, accurate, and affordable DNA bases detection makes it possible to acquire personalized medicine. In this article, a semi-empirical technique is used to calculate the electron transport characteristics of the developed z-shaped graphene device to detect the DNA bases. The z-shaped transistor consists of a pair of zigzag graphene nanoribbon (ZGNR) connected through an armchair graphene nanoribbon (AGNR) channel with a nanopore where the DNA nucleobases are positioned. Non-equilibrium Green's function (NEGF) integrated with semi-empirical methodologies are employed to analyze the different electronic transport characteristics. The semi-empirical approach applied is an extension of the extended Hückel (EH) method integrated with self-consistent (SC) Hartree potential. By employing the NEGF+SC-EH, it is proved that each one of the four DNA nucleobases positioned within the nanopore, with the hydrogen passivated edge carbon atoms, results in a unique electrical signature. Both electrical current signal and transmission spectrum measurements of DNA nucleobases inside the device's pore are studied for the different bases with modification of their orientation and lateral translation. Moreover, the electronic noise effect of various factors is studied. The sensor sensitivity is improved by using nitrogen instead of hydrogen to passivate the nanopore and by adding a dual gate to surround the central semiconducting channel of the z-shaped graphene nanoribbon.