In the early 19th century in the United States, rabbis often wore a scholar's cap (large saucer-shaped caps of cloth, like a beret) or a Chinese skullcap.
Other Jews of this era wore black pillbox-shaped kippot.
Much more common was the simple cloth skullcap, dating back to Egyptian times when those of high society routinely shaved their heads, to prevent lice.
Conversely, their skullcaps then served as protection against irritation from their wigs.
This calls to mind pictures of Syrians on Egyptian monuments, represented wearing a cord around their long, flowing hair, a custom still followed in Arabia.