Iron is mainly made or is the product of decays from nuclear processed material inside supernovae.
As the Earth (and solar system) is around 4.5 billion years old, then the stars that manufactured the iron that is currently in the Earth's core died more than 4.5 billion years ago. Note that the solar system formed out of the gases that had been enriched by the supernova explosions of hundreds of millions of stars all mixed up together.
There are basically two categories of star that can have exploded as supernovae and disseminated this iron into the interstellar medium and from which the solar system could then have formed. The first is massive stars ($>8-10M_{odot}$). These can produce iron and nickel in their cores as a result of silicon burning in the final stages of their evolution. There is then a brief core-collapse followed by an explosion and the resulting supernova can scatter some of this processed, iron-rich material into space.
The remnants of these ancient supernova explosions could be a neutron stars or a black holes. These are almost untraceable/unobservable now, but there should be around a billion of them in our Galaxy.
The second category is the progenitors of what are called type Ia supernovae. These are thought to arise from the thermonuclear explosion of a white dwarf star. White dwarfs are the end point of the evolution of less massive stars. Iron-producing type Ia supernovae $>4.5$ billion years ago, would have begun as stars with masses between about 1.5 and 8$M_{odot}$. These would have burned hydrogen, then helium to produce a degenerate carbon and oxygen core. This core then simply cools and fades away as a white dwarf star in most cases. In type Ia supernovae, some event later in their lives, either mass transfer from a companion, or merger with a companion, caused the white dwarf to exceed its Chandrasekhar mass and triggers an instability that leads to the rapid total consumption of the star in a thermonuclear explosion. The products of this explosion include a large amount of Nickel, that then radioactively decays into Iron. Nothing is left of the white dwarf.
EDIT: Having established this we can begin to look at your edited question. Firstly, the gas and stars in the Galaxy are basically orbiting the Galactic centre. The orbital period at the Sun's radius is about 230 million years, so it has completed many Galactic orbits. Not only that, but it could have migrated in orbital radius as well. There are claims and counter claims in the literature and the issue is not settled. The Sun could have moved in or out by a significant fraction of its current Galactic orbital radius.
The high mass progenitors of core collapse supernovae will have been born (and died) very close to the Galactic plane. The same is not so true of type Ia supernovae, which had longer lived progenitors that could have moved significantly from the Galactic plane before exploding, and indeed would themselves have orbited the Galaxy many times. The gas expelled in a supernova explosion spreads out (over thousands of years) over tens of light years and becomes mixed into the interstellar medium. The interstellar medium is itself stirred and mixed by the energy input from these supernovae, but also due to the heating and winds of other stars, the tides of the galaxy and spiral arms. The interstellar medium appears to be quite homogeneous in terms of chemical composition, though radial gradients exist with scale lengths of order ten thousand light years.
In conclusion, what you ask is almost impossible to answer. The solar system iron almost certainly came from countless supernovae with a variety of progenitors, that would have exploded any time between almost the birth of the Galaxy 11-12 billion years ago (in fact the supernova rate was likely higher then) up until the Sun's birth. The biggest contributors would come from those stars inhabiting an annulus of many thousands of light years across, centered roughly on where the Sun was born, which is itself uncertain.
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