Presumably you have a retainer agreement or representation agreement with your lawyer which states the agreement between the two of you as to what percentage the lawyer may take from the gross recovery. Assuming there is such an agreement, it is what you look to first when attempting to answer the question you have posted.
Not legal advice, just my two cents. I don't practice law in California or hold California licensure. If you need legal advice, please consult a lawyer who does.
Why is this a child support question?
Michael is in San Jose, California and can be reached at 408-295-4232 or at firstname.lastname@example.org. Consultation fees, rates and retainers vary based on need and ability to pay.
The answer is in your written retainer agreement.
The above is general legal and business analysis. It is not "legal advise" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
Being licensed in California and only practicing personal injury, with experience I can say your situation is unfortunate and unfortunately I'm not sure there's anything you can do about it. Contingency fee agreements usually state the attorney is entitled to a percentage of the gross recovery; the ambiguity will be in defining "gross recovery". Apparently your attorney feels that getting a med pay check in counts towards the gross recovery. In reality, it is an attorney's job to get a recovery from the at-fault party and tackle all of the challenges that may be posed in doing so. Getting your own carrier to issue a med pay check based on medical bills is not a recovery from the at-fault party. You may want to check with the State Bar, but I am uncertain there are any ramifications for his/her actions.
Although some attorneys take fees out of med pay (and the written retainer agreement will control), I personally do not and think it is bad form for a lawyer to take 1/3 of a no-fault payment. You may want to consider getting another lawyer to handle the rest of your case.
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