Unveiling the nature of donor stars of ULXs in NGC 1559

X-ray data provide insights into accretion processes and the compact objects of ultraluminous X-ray sources (ULXs), while optical and infrared (IR) observations help identify the donor star and surrounding environment. Together, these approaches shed light on the origins of the high X-ray luminosities observed in ULXs. This study examines the optical and infrared properties of eight ULXs in NGC 1559 using archival data from the Hubble Space Telescope (HST) and James Webb Space Telescope (JWST). To constrain the nature of the donor stars of the ULXs, photometric results were obtained from the temporal, spectral energy distributions (SEDs), and color-magnitude diagrams (CMDs). Furthermore, the long-term and spectral characteristics of only a ULX X-1 were investigated. ULX counterparts were determined from astrometric calculations. The long-term light curves and SEDs were constructed to interpret the origin of the optical and IR emissions. The masses and ages of donor star candidates were determined using CMDs. To constrain the mechanism of X-ray emission, the time-averaged spectrum and long-term light curve of the X-1 were obtained. Unique optical and IR counterparts for ULXs X-14 and X-24 were determined, while only optical counterparts were detected for X-1 and X-18. Our findings indicate that the optical emission originates from the donor stars of X-14 and X-24, whereas for X-1 and X-18, it is dominated by the accretion disk. In addition, the X-1 exhibits long-term X-ray variability spanning orders of magnitude.