Context. Monitoring of BL Lacertae at 15 GHz with the Very Long Baseline Array (VLBA) has revealed a quasi-stationary radio feature in the innermost part of the jet, at 0.26 mas from the radio core. Stationary features are found in many blazars, but they have rarely been explored in detail. Aims. We aim to study the kinematics, dynamics, and brightness of the quasi-stationary feature of the jet in BL Lacertae based on VLBA monitoring with submilliarcsecond resolution (subparsec-scales) over 17 years. Methods. We analysed position uncertainties and flux leakage effects of the innermost quasi-stationary feature and developed statistical tools to distinguish the motions of the stationary feature and the radio core. We constructed a toy model to simulate the observed emission of the quasi-stationary component. Results. We find that trajectories of the quasi-stationary component are aligned along the jet axis, which can be interpreted as evidence of the displacements of the radio core. The intrinsic motions of thecore and quasi-stationary component have a commensurate contribution to the apparent motion of the stationary component. During the jet-stable state, the core shift significantly influences the apparent displacements of the stationary component, which shows orbiting motion with reversals. The quasi-stationary component has low superluminal speeds on time scales of months. On time-scales of few years, the apparent mean speeds are subrelativistic, of about 0.15 the speed of light. We find that the brightness profile of the quasi-stationary component is asymmetric along and transverse to the jet axis, and this effect remains unchanged regardless of epoch. Conclusions. Accurate positional determination, a high cadence of observations, and a proper accounting for the core shift are crucial for the measurement of the trajectories and speeds of the quasi-stationary component. Its motion is similar to the behaviour of the jet nozzle, which drags the outflow in a swinging motion and excites transverse waves of different amplitudes travelling downstream. A simple modelling of the brightness distribution shows that the configuration of twisted velocity field formed at the nozzle of the jet in combination with small jet viewing angle can account for the observed brightness asymmetry.