First, it may be a matter of contract. Second, whether he or she was qualified as an expert witness may have nothing to do with the contract with you. Sometimes court decline to deem a witness a so called expert because of procedural or legal issues, not the quality of the witnesses job and qualifications.
No attorney-client relationship implied or accepted without a signed fee agreement. This response is theoretical only and for purposes of discussion. Attorney is not liable for any opinion expressed herein.
Typically, therapists do not like to get involved in family situations involving a marital dispute for this reason, they know they will be subpoenaed to appear, by one side or the other, be expected to testify as a 'non-expert' (even though they are being presented as a sort of 'semi-expert') and not get paid for their time. The individuals creating the subpoena rationalize this by pretending that the therapists don’t really do anything but talk. My sympathy is with the therapist.
As noted by the earlier answer, most experienced therapists are familiar with this ‘ploy’ and as a condition of providing the therapy, require the responsible party sign a document that spells out the responsibility of the party to reimburse them for their time.
I am licensed in New Mexco and Pennsylvania, and therefore any discussion of issues related to other states must considered within that context. In addition, my comments are not intended to create a legal representation but merely to respond to the limited facts presented in the question. A more complete legal areview can be obtained through local counsel.
Assuming, as you seem to indicate in your clarification, that there is no contract between you and the doctor, then OCGA 24-10-24 governs. Any witness who testifies in response to a subpoena is entitled to a $25 witness fee for that day. If the doctor has been paid that witness fee, then you can ask the doctor--in writing--on what he bases his fee. I am not aware of a statutory right that the doctor would have to being paid his regular rate for testifying under subpoena power.
This answer is not intended to provide legal advice or to be a solicitation. Legal information contained in this answer is for informational purposes only. It is general and should not be relied on as legal advice. Legal advice cannot be given without full consideration of all relevant information concerning an individual situation.