Did Jesus have a cover on the head?

Is there any referring in the holy books regarding Jesus if he covered his head? And if not, based on what a lot of pastors/bishops or pop, cover their head? (of course, different types and forms of covers on the head, I'm not familiar with their specific names) Also, I can see for example in the Orthodox Christianity that only people with function in the church are going with this cover, but other people from their community, although they are absolutely religious, they do not cover their head. And it raises another question if it's only for those who have a function in the church?