Motivated by the existence of helical wrapping patterns in composite nanotube systems, in this work we study the effects of the helical incorporation of carbon atoms in boron nitride nanotubes. We consider the substitutional carbon atoms distributed in stripes forming helical patterns along the nanotube axis. The density of states and energy band gap were calculated adopting Green function formalism by using the Rubio-Sancho technique in order to solve the matrix Dyson equation. We report the effects of the helical atomic distribution of carbon atoms on the behaviour of the density of states and the energy band gap. In particular, we show that the electronic energy band gap displays a non-monotonical dependence on the helical pattern, oscillating as a function of the helical angle θ.