It will not. Once released, the object is in a very slightly different orbit from the space station.
If you put the object further out or further in from Earth than the space station it will be slightly further from, or slightly closer to Earth, while moving at the same velocity as the Space station, which will result in a slightly more, or less elliptical orbit, with a different semimajor axis and orbital period. As a result, it won't be able to remain stationary with respect to the space station
If you put the object ahead, or behind the space station in its orbit, if the space station's orbit is elliptical, the object will be moving too fast, or too slow relative to the space station's orbit to maintain exactly the same orbital path that the space station is travelling, and relative to the space station, the object will drift.
If you put the object perpendicular to the plane of the space station's orbit and release it, the orbit the object is in will have a very slightly different orbital inclination to the space station, and these orbits must cross, as such the distance between the space station and the object cannot remain constant.
Any position you release the object will be a combination of the above cases.
As a result, unless the space station is in a perfect, circular orbit, there is no place on its orbit where you can release an object and have it forever remain at a constant distance from the space station, without orbital adjustments.