A satellite can appear to "stand still" from the perspective of an observer on the ground, so long as it orbits at the right altitude/speed (speed and altitude of an orbit are proportional); the satellite's orbital period just has to be exactly a day long. For Earth, that altitude is about 42,000km up. However, it would still be easily determined to be a nearby satellite as opposed to a distant star by triangulation.

https://en.wikipedia.org/wiki/Geosynchronous_orbit

You're suggesting we fake a signal?

Technically, a satellite could be parked in a Lagrange Point. But the signal would have to be very, very convincing because there will be many, many very smart people looking at it.