Can I get a possession of drugs charge dropped if drugs were found in my car on the passenger side that I knew nothing about?

By dropped, I am assuming you mean dismissed by the prosecutor? That might be possible, but no attorney can predict that without reviewing the evidence in your case and discussing the case with the specific district attorney prosecuting it. Possession means inentionally and knowingly excercising care, custody, control or management of the item. Legal possession cannot be reckless or accidental. If you are not guilty of possessing the drugs, don't plead guilty. Then, hire the attorney you trust to fight your case. I would look to the attorneys reviews, and relevant experience to guide you, but also in person consultations can help you decide.  Good luck.