Can a private pay Certified Nurse Assistant dispense medication per doctors prescription order?

I would check your state laws. Where did u train? Ask them.
In NJ they have to be med techs. In facilities, meds are in blister packs. Easier to keep records of.

It depends on state licensure.  Narcotics may be a no no. So too injections.

In NJ I know CNA’s cannot touch medications..not in our scope of practice..

This is tricky.
A nurse can dispense medication written by a doctor.
A Med Tech or Medical Assistant or CNA can give drugs while working "under" a doctor's license (supervision), usually in the same facility with them.

I don't believe you can dispense them (take them out of the pill bottles, put them in a little cup and put them in her mouth.) But, I *believe* you can hand her the little cup, that the husband has filled and she can swallow them. If SHE takes them then you haven't "given" them. If you pour them into her mouth, then you have "given" them.

That's how I understand it.

I'm no expert but I think it depends on what exactly you mean by dispensing medication, for instance if the husband places her lunchtime meds in a single use container you can hand her the container and a glass of water, anything beyond that is probably not wise. It really is for your own protection so that any medication problems can not be blamed on you.