Only two supported authentication for JIRA which is JIRA default authentication and Crowd SSO authentication. There are many other custom authentication that has been tried and successfully configured by customers such as NTLM, however it is not supported by Atlassian.
Hope it clarifies your doubts on this issue.
Off the shelf, an internal username/password prompt. It then supports LDAP and Crowd lookups natively with minor config tweaks. (Technically, the username/password is Crowd as well, but it's internal) There are plugins that provide more clever stuff and an API to allow you to write your own.
This is kind of a vague question to be honest - there's all sorts of things you could say it "supports" with tweaks to a lesser or greater extent, but it's hard to say it supports any specific type (bar the three above) unless we know what you're looking for.
You can also bring SSO into it of course.
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