Each former Confederate state enacted its own pension system, but the only one I have details on is Arkansas. I assume, but don't know for certain, that most of the state pension systems were similar.

Arkansas enacted "An Act for the Relief of Certain Soldiers of the Late War Between the States" in 1891. The pension system thus established provided relief only to certain veterans and unremarried widows. There was no provision for children, who were well into middle-age by this time.

The Arkansas Confederate pension system was amended many times between 1891 and 1939, but the children of veterans were never included. The only significant expansion of the system beyond veterans and widows occurred in Act 325 of 1905, where widowed mothers of soldiers who "died single" became eligible for a pension.

I understand that U.S. government Civil War pensions had a provision for minor children of deceased soldiers, but I don't know any details. Perhaps someone more knowledgeable than me can throw in and expand on this.