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 (TM), 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 (TM) entry surface doses, relative to D-max, were (9.9 +/- 0.2)%, (10.1 +/- 0.3)%, (11.3 +/- 0.6)%, (12.9 +/- 1.0)%, and (13.4 +/- 1.0)% for 1 x 1 cm(2), 3 x 3 cm(2), 5 x 5 cm(2), 10 x 10 cm(2), and 22 x 22 cm(2) fields, 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 (TM) 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 x 10 cm(2) field size using the MOSkin (TM) and 17.9% for the 22 x 22 cm(2) field size, using Geant4 calculations. The results presented in the study validate the suitability of the MOSkin (TM) detector for transverse MR-linac surface dosimetry.