Let's say a crime is committed on a Venice's merchant colony on Constantinople. Do the Byzantines interfere or it's all on the Venetians? If it's Venetian jurisdiction, who was the authority on such matters (was it appointed by the government, chosen by locals) ?
I say Venice and Constantinople, but I'd be interested in other Merchant Republics and important cities too.
I think in both the Byzantine and later Ottoman empires, the members of trading colonies were tried by their own people. Only exception would be real serious crimes, or crimes committed against a local. The trading colonies were run by an ambassador appointed by the state (Venice in this case). Those individuals had a great deal power, because the trading was largely done under state monopolies. And they also ran religious affairs for the colonists too. It was basically a state within a state.
I don't think the colonies had a separate court system.