That is a mitre, first mentioned in Exodus 28. As for Christ, as Scripture tells us, there is much He said and did which we do not know.
"But there are also many other things which Jesus did; which, if they were written every one, the world itself, I think, would not be able to contain the books that should be written." John 21:25
And one thing we know for certain...Jesus didn't tell you or anyone you know what those things were...So why bring it up??? It doesn't pertain to you...