Summary: We classify the \(3\)-Weierstrass points on genus two curves \[ y^2 = x^6 + ax^4 + bx^2 + 1, \] where \(a,b\in \mathbb{C}\) are parameters. We describe the classification in terms of the invariants \(u=ab\) and \(v=a^3+b^3\) (see [T. Shaska and H. Völklein, in: Algebra, arithmetic and geometry with applications. Papers from Shreeram S. Ahhyankar’s 70th birthday conference, Purdue University, West Lafayette, IN, USA, July 19–26, 2000. Berlin: Springer 703–723 (2003; Zbl 1093.14036)].