We present CCD observations for the distant northern open star clusters Berkeley 81, Berkeley 99, NGC 6603 and NGC 7044 in BVI photometric passbands. A total of 9900 stars have been observed in fields of about 6x6arcmin^2^ of the sky around the clusters. Colour-magnitude diagrams in V, (B-V) and V, (V-I) have been generated down to V=22mag and, for the first time, such diagrams have been produced for the clusters Berkeley 81 and Berkeley 99. The data serve as a base for the study of mass functions and for comparison with theoretical models. Analysis of the radial distribution of stellar surface density indicates that the radius values for Berkeley 81, Berkeley 99, NGC 6603 and NGC 7044 are 2.7, 2.8, 2.8 and 2.2arcmin respectively. By fitting the latest convective core overshooting isochrones to the colour-magnitude diagram and using its morphological features, reddenings, distances and ages of the star clusters have been determined. Broad but well-defined main sequences with stellar evolutionary effects in the brighter stars are clearly visible in colour-magnitude diagrams of all the clusters under study. Some blue stragglers along with well-developed giant branches and red giant clumps are also clearly seen in all of them. The clusters studied here are located at a distance of ~3 kpc, except for Berkeley 99 which is located at a distance of 4.9kpc. Their linear sizes lie between 3.8 and 8.0pc; E(B-V) values range from 0.3 to 1.0mag, while their ages are between 0.5 and 3.2Gyr. Thus the star clusters studied here are of intermediate and high age but are compact and distant objects.