It's likely you meant "posterity".
Posterity refers to:
* Future generations: The people who will live after the present time.
* The descendants of a person: The children, grandchildren, and so on of a particular individual.
For example:
* "She wrote her memoirs hoping to leave a legacy for posterity."
* "The monument was built to honor the memory of those who died for the cause, for all posterity to remember."