The content of extremely high energy (EHE) photons in the highest energy cosmic rays can be investigated by analyzing showers arriving from directions where the perpendicular component of the Earth's magnetic field is high or showers arriving from the region surrounding the Sun. We perform Monte Carlo simulations of cascades initiated by photons with parameters of the highest energy showers observed by the past and present detectors (AGASA, Fly's Eye, Yakutsk, Haverah Park). The purpose is to find out which events should cascade with high probability if initiated by photons. It is shown that EHE photons arriving from directions towards the magnetic poles cascade with higher probability. Alternatively, the lowest probabilities of cascading are expected for photons arriving from directions of the equator at the zenith angles equal to the angle between location of the specific observatory and the magnetic pole. We show that very unusual showers should arrive from direction of the Sun due to cascading of photons in the Sun's magnetosphere if EHE photons are numerous at the highest energies. The rate of such showers is estimated on about one per ten years. However extraordinary lateral distribution of secondary particles of such showers in the Earth's atmosphere may help to distinguish them from the ordinary showers arriving isotropically from the sky.