Continuous gravitational waves (CWs) emission from neutron stars carries information about their internal structure and equation of state, and it can provide tests of general relativity. We present a search for CWs from a set of 45 known pulsars in the first part of the fourth LIGO–Virgo–KAGRA observing run, known as O4a. We conducted a targeted search for each pulsar using three independent analysis methods considering single-harmonic and dual-harmonic emission models. We find no evidence of a CW signal in O4a data for both models and set upper limits on the signal amplitude and on the ellipticity, which quantifies the asymmetry in the neutron star mass distribution. For the single-harmonic emission model, 29 targets have the upper limit on the amplitude below the theoretical spin-down limit. The lowest upper limit on the amplitude is 6.4 × 10−27 for the young energetic pulsar J0537−6910, while the lowest constraint on the ellipticity is 8.8 × 10−9 for the bright nearby millisecond pulsar J0437−4715. Additionally, for a subset of 16 targets, we performed a narrowband search that is more robust regarding the emission model, with no evidence of a signal. We also found no evidence of nonstandard polarizations as predicted by the Brans–Dicke theory.