In order to have a realistic organism capable of creating halfbreeds, all species involved must have a VERY close common ancestor.
As an example, consider real dogs. A Chihuahua and a Great Dane are incapable of directly breeding without artificial insemination due to geometric isolation. If there were no other breeds of dogs between them to bridge the gap, they would be considered different species. However, both of these dogs could breed with some third dog of medium size.
Assuming you are looking at a science fiction setting, this probably means that all your alien species are human derivatives. This can occur if inter stellar travel is slow/rare, which would cause distant colonies to act as isolated populations. There are two ways that these isolated groups could have diverged.
They could simply have evolved differences over a very long time. This would probably work best over a period of ten thousand to a hundred thousand years. That is probably long enough to create significant phenotypic differences without necessarily developing any insurmountable genetic incompatibilities. 1008
To keep the populations separate long enough, you would probably need for the secret of spacetravel to have become lost for some reason. As an additional advantage, it is far enough back that it would not have interfered with recorded history. Moreover, you could jump directly from modern humanity to your desired tech level by finding the ruins of an advanced ancient civilization someplace on earth.
The other option is that the difference has arisen due to self applied genetic engineering. This cuts down the required isolation period to a few hundred years for the first few generations at each colony to have died off. Isolation on a timescale like this can be simply explained with a slow interstellar drive. If you want a much quicker drive for your plot, that can have been a far more recent invention. The other advantage of this is that your species can be FAR more anatomically different without the differences being insurmountable to genetic engineering.
If you are operating in a fantasy setting, things become easier. You can set up all of your races as sharing human genetics. Racial differences can be explained in this setup as being caused by heritable enchantments. 1008