  Current study is focussed to discuss the existence of a new family of compact
star solutions by adopting the Karmarkar condition in the background of Bardeen
black hole geometry. For this purpose, we consider static spherically symmetric
spacetime with anisotropic fluid distribution in the presence of electric
charge. We consider a specific model of $g_{rr}$ metric function, to describe a
new family of solutions which satisfies the Karmarkar condition. Further, we
investigate the interior solutions for two different models of compact stars
with observational mass and radii, i.e., $(M=1.77M_{\odot}, \;R_{b}=9.56km)$
and $(M=1.97M_{\odot}, \;R_{b}=10.3km)$. It is found that these solutions
fulfill all the necessary conditions for a charged star. Through graphical
discussion, it is noticed that our calculated solutions are physically arguable
with a best degree of accuracy for $n\in[1.8,7)$, where parameter $n$ is
involved in the model under discussion. However, it is perceived that the
presented model violates all the physical conditions for $n\in\{2,4,6\}$.
Finally, it is concluded that the parameter $n$ has a strong impact on the
obtained solutions in the context of Bardeen stellar structures.
