* Genesis Mission (NASA): This was a mission launched in 2001 to collect solar wind particles. It returned to Earth in 2004. It's possible you're thinking of this mission.
* The Genesis Project (private): This is a private initiative that aims to build a "Space Ark" to preserve human and animal DNA in case of an Earth-wide catastrophe. It's not a specific space mission, but a larger project.
Could you please clarify what you mean by "Genesis Space Mission"? Providing more context would help me give you a more accurate answer.
