Among all continua joining non-collinear points a 1, a 2, a 3 ∈ ℂ, there exists a unique compact Δ ⊂ ℂ that has minimal logarithmic capacity. For a complex-valued non-vanishing Dini-continuous function h on Δ, we define $${f_h}(z): = \frac{1}{{\pi i}}\int_\Delta {\frac{{h(t)}}{{t - z}}\frac{{dt}}{{{w^ + }(t)}}} $$ , where $$w(z): = \sqrt {\prod\nolimits_{k = 0}^3 {(z - {a_k})} } $$ and w + is the one-sided value according to some orientation of 1. In this work, we present strong asymptotics of diagonal Padé approximants to f h and describe the behavior of the spurious pole and the regions of locally uniform convergence from a generic perspective.