ABSTRACT Gaia Data Release 2 revealed a population of ultramassive white dwarfs on the Q branch that are moving anomalously fast for a local disc population with their young photometric ages. As the velocity dispersion of stars in the local disc increases with age, a proposed explanation of these white dwarfs is that they experience a cooling delay that causes current cooling models to infer photometric ages much younger than their true ages. To explore this explanation, we investigate the kinematics of ultramassive white dwarfs within 200 pc of the Sun using the improved Gaia Early Data Release 3 observations. We analyse the transverse motions of 0.95–1.25 M⊙ white dwarfs, subdivided by mass and age, and determine the distributions of the three-dimensional components of the transverse velocities. The results are compared to expectations based on observed kinematics of local main-sequence stars. We find a population of photometrically young (∼0.5–1.5 Gyr) ultramassive (∼1.15–1.25 M⊙) white dwarfs for which the transverse velocity component in the direction of Galactic rotation is more dispersed than for local disc stars of any age; thus, it is too dispersed to be explained by any cooling delay in white dwarfs originating from the local disc. Furthermore, the dispersion ratio of the velocity components in the Galactic plane for this population is also inconsistent with a local disc origin. We discuss some possible explanations of this kinematically anomalous population, such as a halo origin or production through dynamical effects of stellar triple systems.