If you mean 'space' as in the more or less vacuum existing between planets and stars etc.
Then any kind of evolution is impossible because evolution is gradual adaptation over many generations.
A solitary organism does not evolve.
It might be possible for simple organisms like those on Earth to survive if they were placed in spaces, but not to evolve.
Space has no liquid water and only microscopic amounts of other nutrients which an organism needs to produce offspring.
Apart from one extremely speculative idea, I am not aware of any serious proposal how that is supposed to work. You need matter for life, and you need mechanisms to re-arrange that matter in controlled ways. Both things are rarely possible in space.