The jeely piece is the Glasgow jam sandwich, and the word is the whole of its identity. A "piece" is Scots for a sandwich carried out of the house to be eaten elsewhere, and "jeely" is jelly, meaning jam, so the name is a tenement description before it is a recipe: the jam piece you took to school, to the back court, or up the close. It is the same build as a jam sandwich, soft bread, butter, jam, but it belongs to a specific place and a specific way of life, and that belonging is what makes it its own thing rather than a regional spelling. It is the sandwich of the high flats, handed down to children playing below, and it carries that whole world in two syllables.
The craft is the same restraint every good jam build relies on, read through the conditions it was made for. The butter goes on firm and to the edges as a waterproof seal, because a piece is by definition food that travels and a piece that bleeds jam through the bread before the child reaches the bottom of the stairs has failed at its one job. The jam is spread thin over the butter, never straight onto the slice, so it does not squeeze out when the piece is folded into a hand or a pocket. The bread is plain soft white, the cheap loaf that was in the house, and it is not toasted or dressed up, because the point of a piece was never refinement; it was a sweet thing made from what there was, made to be carried, and made to keep a child going until tea.
The variations are the larder and the dialect rather than a change of idea. A jam piece, a sugar piece, a piece on condensed milk, a piece and cheese: the same carried-sandwich logic with whatever was in the press. The plain jam sandwich is the wider British form of the same build without the Glasgow identity attached. Each of those deserves its own article rather than being crowded in here.