Electromagnetic behavior of twisted clad optical fiber structure is investigated under the situation of core section being composed of chiral nihility metamaterial. Twists in the fiber clad are introduced in the form of sheath helical conductor loadings at the core-clad interface. The dispersion relation for the fiber structure is deduced and analyzed (considering low-order sustained hybrid modes) in respect of the effect on the dispersion characteristics due to the alterations in helix pitch angle. It have been found that the fiber structure generally shows decrease in normalized propagation constant with the increase normalized frequency parameter. Also, the dispersion behavior is greatly affected due to the variations in the angle of twists in the helix pitch.