We investigate asymptotic behavior of polynomials $$ Q_n(z) satisfying non-Hermitian orthogonality relations $$\begin{aligned} \int _\Delta s^kQ_n(s)\rho (s)\textrm{d}s =0, \quad k\in \{0,\ldots ,n-1\}, \end{aligned}$$ where \Delta is a Chebotarëv (minimal capacity) contour connecting three non-collinear points and \rho (s) Jacobi-type weight including possible power-type singularity at the cen...