Gaia Data Release 2 revealed the presence of a population of ultramassive white dwarfs on the Q branch that are moving anomalously fast for a local disc population with the cooling ages determined using white dwarf cooling models, which has been presented as evidence of an extra cooling delay experienced by these white dwarfs. In this work, we investigate the kinematics of ultramassive white dwarfs in the solar neighbourhood using the improved Gaia Early Data Release 3 observations to explore this cooling delay explanation and alternate possibilities. We performed a kinematic analysis of the transverse motions of 0.95-1.25 $M_\odot$ white dwarfs within 200 pc of the Sun subdivided by mass and age and compared the result to the expectation based on the observed kinematics of main sequence stars. The distributions of the transverse velocity component in the direction of Galactic rotation for different mass and age ranges reveal a population of photometrically young ($\sim$ 0.5-1.5 Gyr) ultramassive ($\sim$ 1.15-1.25 $M_\odot$) white dwarfs that lags the local Galactic rotation and that is too dispersed in this velocity component to be explained by a cooling delay in white dwarfs originating from the local Galactic disc. 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.