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 cm2fields, respectively. For the investigated fields, the maximum percent differences of Geant4, TPS, and film doses extrapolated and interpolated to a depth suitable for skin dose assessment at the beam entry, relative to MOSkin™ measurements at an equivalent depth were 1.0%, 2.8%, and 14.3%, respectively, and at a WED of 199.67 mm at the beam exit, 3.2%, 3.7% and 5.7%, respectively. The largest measured increase in exit dose, due to the electron return effect, was 15.4% for the 10 × 10 cm2field size using the MOSkin™ and 17.9% for the 22 × 22 cm2field size, using Geant4 calculations. The results presented in the study validate the suitability of the MOSkin™ detector for transverse MR-linac surface dosimetry.