Health & Safety Code 11350 is possession of certain controlled substances, such as cocaine and heroin. It is a felony punishable by up to three years in state prison. H&S 11351 is possession of the same drugs for sale, with a potential for four years in prison.
A conviction for 11351 is considered an aggravated felony, which is the worst possible kind of conviction for immigration purposes. You could be deported, and would never be able to return to the United States.
Even a conviction for simple possession under 11350 is a big problem, and would subject you to deportation and make you inadmissible. This is true of all drug possession offenses; the only exception for drug offenses is a first offense for possession of less than an ounce of marijuana.
There are diversion programs that could avoid a conviction... but in most of them, you could be deported until you complete the program.
Your stakes are high and it's impossible for anyone to give you meaningful advice without more information... and you should NOT post more details on the Internet where everyone can read them.
You need a lawyer to help you with this case, not generic advice from a stranger on the Internet. The United States Supreme Court says criminal defense attorneys must be able to advise their clients about the possible immigration consequences of a conviction. Most public defenders have good training in this area; if you don't qualify for the public defender or decide to hire your own attorney, make sure you lawyer knows about immigration law and works with your immigration attorney.
I agree completely with Mr. Marshall. He is not trying to scare you but to tell you the truth. Anything else and he would do better to keep his mouth shut. I don't know who you consider the Best Lawyer in CA but Mr. Marshall is certainly one. I hope you are not negotiating with a state wide law firm run in Johnny Cochran's name who will convince you that he or someone like him will try your case. If you are be aware you are not talking to the best attorneys in CA.
You are dealing with some hacks who will take everything you've got and then farm your case out to a beginner for a $2,000 fee. Watch out!!!