You can use any milk to make coffee with milk, but whole-fat milk is the best option since it yields a creamy and filling texture and a milder taste.

Of course, you can if you want, but Turkish coffee is traditionally drunk without adding cream or milk. İnstead of adding milk to it, you can make it with milk instead of water as explained on this page.

To make Turkish coffee with milk, you should follow the regular Turkish coffee making process but add cold milk instead of cold water. Turkish coffee milk to coffee ratio is the same as water to coffee ratio. So, you should add 2 teaspoons of ground Turkish coffee for each cup of milk and gently stir them before placing the coffee pot on the stove. Then, you should wait for ground coffee to dissolve into the milk. Coffee particles would better dissolve if you stir it occasionally.

You should not use electric cezve to make Turkish coffee with milk because they are designed only to make coffee with water. On the other hand, to make Turkish coffee with milk using an automatic Turkish coffee maker is not a good option, either, since its sensors are adjusted to make Turkish coffee with water. So, the result you get will not be satisfactory and the machine may break down.