We give conditions for when the fixed points by the partial Atkin-Lehner involutions on $X_0(N)$ are Weierstrass points as an extension of the result by Lehner and Newman . Furthermore, we complete their result by determining whether the fixed points by the full Atkin-Lehner involutions on $X_0(N)$ are Weierstrass points or not.
"Notes on Weierstrass Points of Modular Curves $X_0(N)$." Taiwanese J. Math. 20 (6) 1275 - 1293, 2016. https://doi.org/10.11650/tjm.20.2016.6547