Information about Small Claims Cases in the Harris County Justice of the Peace Courts. Q. How much does it cost to file a Small Claims suit?The Justice of the Peace must collect fees for the filing of a suit in the Small Claims Court. If you're looking for an educated guess, any lawyer here will do. How do I update my address with your office? To get connected with a lawyer, call 7132280735 or fill out a questionnaire online. Houston Lawyer Referral Service.