Using Subaru Hyper Suprime-Cam (HSC) year 1 data, we perform the first -cut cosmic shear analysis constraining both and Hu-Sawicki modified gravity. To generate the cosmic shear theory vector, we use the matter power spectrum emulator trained on COLA (COmoving Lagrangian Acceleration) simulations [Phys. Rev. D 103, 123525 (2021)PRVDAQ2470-001010.1103/PhysRevD.103.123525. The -cut method is used to significantly down-weight sensitivity to small scale modes in the matter power spectrum where the emulator is less accurate, while simultaneously ensuring our results are robust to baryonic feedback model uncertainty. We have also developed a test to ensure that the effects of poorly modeled small scales are nulled as intended. For we find , while the constraints on the modified gravity parameters are prior dominated. In the …