"at THE moment" = right now "in a moment" = soon / "just a minute" / "hold on" "at A moment" is not a common phrase. Maybe you mean "at a moment's notice"?

'at' refers to a fixed point in time. 'At a moment' is actually quite an unusual phrase on its own - we'd be more likely to say eg a certain moment, a particular moment, at any moment. For example: At a certain moment in the film, we suddenly realise who the killer is. 'in' refers to a period of time, usually starting now. For example: 'Hold on. I'll be with you in a moment.'