What is the furthest known star from our solar system?
There is no single "furthest known star".
We know of galaxies that are billions of light years away, which are made up of stars, though we are not able to resolve individual stars. We can resolve a few individual stars in galaxies that are tens of millions of light years away, and these stars have obscure catalog numbers.
But we can also see novae and supernovae in much more distant galaxies, which are also very distant, individual stars.
So we can see groups of stars billions of light years away, and many individual stars even millions of light years away. So it would be exceedingly difficult to identify the "farthest known star".
However, I will suggest a candidate: SDSS J1229+1122, a blue supergiant star in the tail of the dwarf galaxy IC3418, at a distance of 55 million light years.