If i enter the us from europe will i be detained at the AİRPORT checkpoint security for not paying child support for 18 years

As far as entering the U.S. , it may be a problem or not be a problem. But if you exit the U.S., you may find that your passport has been revoked. Failure to pay child support will cause driver's licenses, professional licenses and passports to be subject to revocation. 

U.S. Customs and Border Protection (CBP) primarily focuses on immigration and customs enforcement. While they have access to various law enforcement databases, their primary role does not include enforcing child support orders. The government does not tell us what is on their databases, but it is possible that if there is an active arrest warrant related to unpaid child support, it could be entered into national databases accessible to CBP officers. In such cases, upon re-entry to the U.S., CBP could possibly detain and refer the person to the appropriate law enforcement agency. Due to the limitations of the Lawyers.com Forums, Alan Lee & Arthur Lee, Esqs.’ (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.