The AJ modifier would be correct. I am not familiar with the AH modifier and couldn't find any info on it. I found two different uses for the UD modifier, but neither fits your description.
1: When billing for the attending ED physician E&M service, the modifier UD must be used with the appropriate E&M procedure code to designate that the patient was released (discharged) from the ED
2: Use the “UD” modifier for any physician-administered drugs billed with J codes