Manual:$wgCookieSetOnAutoblock

Details
The cookie that is set will expire when the block expires or after, whichever is shorter (the latter defaults to 30 days). This means that cookies for infinite blocks will also expire at this shorter time.

The cookie is named 'BlockID', prefixed with. It's value is just the block's ID and no other data.

For users with LocalStorage support, a matching entry is created in LocalStorage. In case the cookie is deleted, it will be recreated from this (at the time when the user opens the page-editing form).