The gap structure of a novel uranium-based superconductor UTe 2 , situated in the vicinity of ferromagnetic quantum criticality, has been investigated via specific-heat C(T, H,) measurements in various field orientations. Its angular (φ, θ) variation shows a characteristic shoulder anomaly with a local minimum in H a at moderate fields rotated within the ab and ac planes. Based on theoretical calculations, these features can be attributed to the presence of point nodes in the superconducting gap along the a direction. Under the field orientation along the easy-magnetization a axis, an unusual temperature dependence of the upper critical field at low fields together with a convex downward curvature in C(H) were observed. These anomalous behaviors can be explained on the basis of a nonunitary triplet state model with equal-spin pairing whose T c is tuned by the magnetization along the a axis. From these results, the gap symmetry of UTe 2 is most likely described by a vector order parameter of d(k) = (b + ic)(k b + ik c).