To me that looks like a British army officer's rank badge.
Junior officers wear one "pip" for 2nd Lt, 2 for Lt and 3 for Captain, in a line. Before WW2 many regiments had metal rank pips with a regimental design on them. They had two metal loops underneath which would be pushed through the cloth on the shoulder strap, then held in place with a dark metal split pin, just like the one attached to your badge. The outer star-part for the rank pips were very similar. The inner design varied according to regiment, but often had an enamelled an design like yours. If you can make out the lettering or the inner design, it should be possible to ID the regiment.
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