The magnetic field of a transverse MR-linac alters electron trajectories as the photon beam transits through materials, causing lower doses at flat entry surfaces and increased doses at flat beam-exiting surfaces. This study investigated the response of a MOSFET detector, known as the MOSkin™, for high-resolution surface and near-surface percentage depth dose measurements on an Elekta Unity. Simulations with Geant4 and the Monaco treatment planning system (TPS), and EBT-3 film measurements, were also performed for comparison. Measured MOSkin™ entry surface doses, relative to dmax, were (9.9 ± 0.2) %, (10.1 ± 0.3) %, (11.3 ± 0.6) %, (12.9 ± 1.0) %, and (13.4 ± 1.0) % for 1 × 1 cm2, 3 × 3 cm2, 5 × 5 cm2, 10 × 10 cm2, and 22 × 22 cm2 fields, respectively. Similarly at the beam exit MOSkin™ doses were (37.2 ± 4.9) %, (50.0 ± 2.9) %, (54.9 ± 2.0) %, (63.9 ± 1.6) %, and (62.4 ± 3.0) %. For the investigated fields, the maximum absolute dose differences for Geant4, TPS, and film at the beam entry, relative to MOSkin™ surface doses, were 1.0%, 16.4%, and 24.3%, respectively and at the beam exit, 5.0%, 3.1%, and 5.7%, respectively. The largest increase in exit dose, due to the electron return effect, was 18.0% for the 22 × 22 cm2 field size, using Geant4 calculations. The results presented in the study validate the suitability of the MOSkin™ detector for transverse MR-linac surface dosimetry.