Although it is highly appealing, I am uncertain about the artist who painted this miniature portrait. It is certainly American and highly unusual to show a boy holding a toy gun. Normally, boys were depicted with a hoop, whip, top, or toy horse, whereas girls were depicted with flowers or a doll.
The miniature is housed in a red leather case and the ivory is 112mm x 84mm. Boys wore clothing like this for a number of years from about 1790, but I believe it is later than that, probably about 1820 and from the North East United States.
It is possibly by Anson Dickinson. I say that as the cases of some of his early works show a print of a child on the silk lining. However, that is far from certain and it is hoped a collector of American miniature portraits can suggest the artist.
I do not think it is by Nathaniel Rogers as differences of style can be seen by comparison with this miniature of three children painted by Rogers c1820, where the boy has a similar collar, for more about that see View
In fact although Rogers was very clever in painting heads, his figures are somewhat awkward in comparison, with the pose of the central child here strained, compared to the natural pose of the boy holding a gun.
As always, it is frustrating not to know the name of the sitter and unfortunately there are no clues here. 1453