First of all, administrative detention for fifteen days belongs to administrative punishment, not criminal record. Therefore, under normal circumstances, it will not have an impact on taking the judicial examination and engaging in legal-related industries. But the specific situation needs to be judged according to relevant laws, regulations and policies.
Secondly, if you have taken the judicial examination during administrative detention and passed the examination, then your examination results are valid. However, if you do not take the judicial examination during administrative detention, your examination results may be affected. In addition, those who have been engaged in law-related industries during administrative detention may have their work experience recorded in the file. However, this will not have much impact on your career development.
Finally, if you have any questions about the specific situation, I suggest you consult the relevant legal professionals or the staff of relevant departments to get more accurate and detailed information and suggestions.