Will be deported right away by that judge for overstaying?

Typically, a jury duty summons does not result in a deportation. The worst that could happen is you are placed in removal proceeding where you can ask the Immigration Court to allow you to stay based upon your unique facts. Jury summons have to do with civil or criminal courts not affiliated with the Immigration Court. You may want to try and contact the clerk and explain the situation. Usually, you can avoid even having to show up in connection with the jury summons. It is very important you are honest about your status as claiming to be a U.S. citizen can cause adverse factors.