To emphasize the act of claiming:
* Re-: Indicates repeating the act of claiming, as in reclaim.
* Pre-: Indicates claiming something before something else, as in preclaim.
* Counter-: Indicates claiming something in opposition to another claim, as in counterclaim.
* Sub-: Indicates claiming something that is subordinate to another claim, as in subclaim.
To modify the meaning of "claim":
* Dis-: Indicates the opposite of claiming, as in disclaim.
* Mis-: Indicates a false claim, as in misclaim.
* Over-: Indicates claiming more than what is rightfully owed, as in overclaim.
* Un-: Indicates not claiming something, as in unclaimed.
Other potential prefixes:
* Co-: Indicates claiming something jointly with someone else, as in coclaim.
* Pro-: Indicates claiming something in favor of something else, as in proclaim.
The best prefix to use will depend on the specific context and the desired meaning.