An AI built a city on a single tile island. I can not besiege the city. However, I remember the city was first built by independent people. Any idea how AI took the city, or how I can siege this city?

No idea how to besiege it, but you can take Independent People cities by paying them with money/influence to gain relations and then using influence to assimilate them.

Might need to use a warship and not land units to attack it.

If these single tile sea cities persist in the lunch version of this game, then Amplitude needs to allow dedicated ship units to be able to attack land units standing on land.