Chrome 41 ERR_SSL_VERSION_OR_CIPHER_MISMATCH Tomcat 7

I had the same problem with my Java EE web application running with a self signed certificate on Wildfly 8.1.

You are probably using a 1024 bit DSA public key with your selfsigned certificate and Chrome stops/stopped supporting DSA(DSS).

Creating a RSA 2048 certificate and using it with your web application should solve your problem.

I doubt its an SSL/TLS protocol version problem. Most of the time this error means the server and client couldn't agree on which cipher to use. Take a look at this blog post: https://blog.eveoh.nl/2014/02/tls-ssl-ciphers-pfs-tomcat/ on how to enable a secure and compatible cipher suite in Tomcat.

In the Tomcat server.xml file you can set ciphers attribute in the SSL/TLS <connector/> element.

ciphers="TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256,          TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA,         TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384,         TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA,         TLS_ECDHE_RSA_WITH_RC4_128_SHA,         TLS_RSA_WITH_AES_128_CBC_SHA256,         TLS_RSA_WITH_AES_128_CBC_SHA,         TLS_RSA_WITH_AES_256_CBC_SHA256,         TLS_RSA_WITH_AES_256_CBC_SHA,         SSL_RSA_WITH_RC4_128_SHA"

This solved the problem in my case for ERR_SSL_VERSION_OR_CIPHER_MISMATCH in Chromium / Chrome and for ssl_error_no_cypher_overlap in Firefox.