Context. Detection of the electromagnetic emission from coalescing binary neutron stars (BNS) is important for understanding the merger and afterglow. Aims. We present a search for a radio counterpart to the gravitational-wave (GW) source GW190425, a BNS merger, using Apertif on the Westerbork Synthesis Radio Telescope (WSRT). Methods. We observed a field of high probability in the associated localisation region for three epochs at ΔT = 68, 90, 109 d post merger. We identified all sources that exhibit flux variations consistent with the expected afterglow emission of GW190425. We also looked for possible transients. These are sources that are only present in one epoch. In addition, we quantified our ability to search for radio afterglows in the fourth and future observing runs of the GW detector network using Monte Carlo simulations. Results. We found 25 afterglow candidates based on their variability. None of these could be associated with a possible host galaxy at the luminosity distance of GW190425. We also found 55 transient afterglow candidates that were only detected in one epoch. All of these candidates turned out to be image artefacts. In the fourth observing run, we predict that up to three afterglows will be detectable by Apertif. Conclusions. While we did not find a source related to the afterglow emission of GW190425, the search validates our methods for future searches of radio afterglows.