I wonder how this would work if one parent lived in the Federation and one lived, with the child, in a capitalist society.
Would they be out of luck? Would the Federation pay out on the absent parent's behalf(we already know they have reserves of other currencies, and also have "Federation credits" for trade with capitalist societies)?
The UFP has a currency - Federation Credits. The average citizen may not need (or even have) money, but it exists and is presumably accessible in some way if you have genuine need. For example the station personnel on DS9 never had issues paying at Quark's, so one can assume that they did get a salary because they were posted to a capitalist environment. I'd assume that child support would work on a similar "as needed" basis.
I suppose the child gets a claim to any personal effects of the parent. If the parents role in society offers any boons not available to an ordinary citizen maybe those too.
But in this situation it would probably just be a free shot at joining Starfleet.
There isn't, except when there is. And when there is, they're called credits, but you can't spend them in the Federation, except (I guess) at starbases like Space Station K7, so it's not entirely clear why other governments consider them to have value.
I just wanted you to know that I save these for later, and having the captions be several seconds into the gif is part of the humor. But damn does it make it hard to find/remember which ones have which burn in them.