Low-mass young stellar population and star formation history of the cluster IC 1805 in the W4 H{\sc ii} region

W4 is a giant H{\sc ii} region ionized by the OB stars of the cluster IC~1805. The H{\sc ii} region/cluster complex has been a subject of numerous investigations as it is an excellent laboratory for studying the feedback effect of massive stars on the surrounding region. However, the low-mass stellar content of the cluster IC~1805 remains poorly studied till now. With the aim to unravel the low-mass stellar population of the cluster, we present the results of a multiwavelength study based on deep optical data obtained with the Canada-France-Hawaii Telescope, infrared data from 2MASS, $Spitzer$ Space Telescope and X-ray data from $Chandra$ Space Telescope. The present optical dataset is complete enough to detect stars down to 0.2~M$_\odot$, which is the deepest optical observations so far for the cluster. We identified 384 candidate young stellar objects (YSOs; 101 Class I/II and 283 Class III) within the cluster using various colour-colour and colour-magnitude diagrams. We inferred the mean age of the identified YSOs to be $\sim$ 2.5 Myr and mass in the range 0.3 - 2.5 M$_\odot$. The mass function of our YSO sample has a power law index of -1.23 $\pm$ 0.23, close to the Salpeter value (-1.35), and consistent with those of other star-forming complexes. We explored the disk evolution of the cluster members and found that the diskless sources are relatively older compared to the disk bearing YSO candidates. We examined the effect of high-mass stars on the circumstellar disks and found that within uncertainties, the influence of massive stars on the disk fraction seems to be insignificant. We also studied the spatial correlation of the YSOs with the distribution of gas and dust of the complex to conclude that IC 1805 would have formed in a large filamentary cloud.