Could be Radio Cairo Egypt, on or near 6270 kHz AM. Programming includes prayer several times a day, music and news. Their signal typically has a strong carrier with poor modulation, ranging from weak (despite the powerful carrier) to overmodulated and distorted. And their signal isn't always dead center on frequency but doesn't normally drift more than 1 kHz off nominal freq.
There are several slop-broadcasters in the general 49m band, between 5800-6200, so it's not unusual to pick up phantom carriers, heterodynes and images. WYFR and some RHC transmitters are notorious slop-casters and it's possible that Radio Cairo's signal has some slop as well, which may account for hearing carriers or heterodynes that appear some distance away from nominal frequencies.