Questar M-17 was an object beyond the fringe of the Milky Way Galaxy. It was believed to be the source of mysterious radio emisions until 2269, when during a star charting mission heading on an outward course towards it, the USS Enterprise was drawn of course towards the real source, a second object.

This second object was an unusual dead star, with negative mass and intense hypergravity. A spectral analysis of the star revealed imploded matter, on which every reading was negative as well. Its surface appeared cratered. It also had some magnetic force. It was too far away from any G1 stars to be reached using sub-warp travel.

On stardate 5221.3, the USS Enterprise discovered the dead star while star charting. It was forced to go into orbit due to the object's hypergravity, after which the crew discovered an ancient vessel also in orbit.

A magnetic organism living inside the ancient ship returned to the Enterprise along with the away team and subsequently took control of that vessel. The Enterprise escaped, trapping the organism in Questar M-17's magnetic field. (TAS: "Beyond the Farthest Star")

The dead star might have been beyond the galaxy, as the Enterprise was on outward course beyond its fringe, and part of a spiral galaxy-like object can be seen in the background of one shot of it.
According to Star Trek Maps ("Chart A"), Questar M17 was located near the disputed border between the United Federation of Planets and the Tholian Assembly on the Federation side.
According to Star Trek: Star Charts (p. 13) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), "Quasar M17" was located in the Beta Quadrant, at the fringe of the Milky Way Galaxy, near the galactic barrier.