This paper investigates the effect of charge on traversable wormhole geometry in the context of $ f(\mathcal{G}) $ gravity, where $ \mathcal{G} $ is the Gauss-Bonnet term. Using the embedding class-I technique, the authors examine static spherical spacetime with anisotropic matter configuration to investigate wormhole geometry. The Karmarkar condition is used to develop a shape function for the static wormhole structure. Using this shape function, they construct a wormhole geometry that satisfies all required constraints and connects asymptotically flat regions of spacetime. The study reveals that viable traversable wormhole solutions exist in this modified theory. The paper discusses the behavior of energy conditions for various models of $ f(\mathcal{G}) $ gravity. It also examines three different models of $ f(\mathcal{G}) $ gravity to find exact solutions of static spherical spacetime. The results show that the newly developed shape function through the Karmarkar condition satisfies all necessary conditions for physically viable wormhole geometry. The energy conditions are analyzed for different models, and it is found that the presence of exotic matter is necessary for the existence of traversable wormhole geometry. The study concludes that viable traversable wormhole structures can be obtained in $ f(\mathcal{G}) $ gravity.This paper investigates the effect of charge on traversable wormhole geometry in the context of $ f(\mathcal{G}) $ gravity, where $ \mathcal{G} $ is the Gauss-Bonnet term. Using the embedding class-I technique, the authors examine static spherical spacetime with anisotropic matter configuration to investigate wormhole geometry. The Karmarkar condition is used to develop a shape function for the static wormhole structure. Using this shape function, they construct a wormhole geometry that satisfies all required constraints and connects asymptotically flat regions of spacetime. The study reveals that viable traversable wormhole solutions exist in this modified theory. The paper discusses the behavior of energy conditions for various models of $ f(\mathcal{G}) $ gravity. It also examines three different models of $ f(\mathcal{G}) $ gravity to find exact solutions of static spherical spacetime. The results show that the newly developed shape function through the Karmarkar condition satisfies all necessary conditions for physically viable wormhole geometry. The energy conditions are analyzed for different models, and it is found that the presence of exotic matter is necessary for the existence of traversable wormhole geometry. The study concludes that viable traversable wormhole structures can be obtained in $ f(\mathcal{G}) $ gravity.