General:
* Je connais mon...: This is the most general translation, meaning "I know my..." and can be used in many contexts.
* Je sais mon...: This means "I know my..." but implies more of a factual knowledge, like knowing a fact or a rule.
Specific examples:
* Je connais mon chemin: I know my way
* Je connais mon rôle: I know my role
* Je connais mes limites: I know my limits
* Je sais mon histoire: I know my history
* Je sais mes droits: I know my rights
Important note: The best translation will depend on the specific context of the phrase "I know my".