Websocket SSL Client Certificates Authentication in Mobile Web browsers

I start a server at X.X.X.X:8080 with two-way authentication using Tornado, and in the main page's JavaScript I start a websocket that communicate with my server, address is "wss://X.X.X.X:8080/ws".

Everything works fine in desktop browsers, but not my iPhone.

I installed my server's ca.crt and client.p12 profile onto my iPhone and opened https://X.X.X.X:8080, the main page and all the script can be accessed, which means the client side can establish the right TLS communication with my server, but the websocket was closed as soon as it was created. On the server side, it prompted PEER DID NOT RETURN CERTIFICATE.

So I'm wondering if websocket SSL client certificate authentication is supported in Mobile Web browsers.

My site is tested on iPhone 6S with iOS 10.2.