I want to set up size for my tasks and stories based on t-shirt sizes convention. I can't find it in Jira Kanban board. Does Jira support it?
You can create a custom field. But are you sure you want to do that?
The Story Points field for Issues in Jira Agile will accept only numerical values. However, if you are particular, you can create a custom field that will accept T-shirt sizes. However, please keep in mind that you won't be able to compute sprint velocity. As a consequence you won't be able to judge what is a realistic team commitment.
Teams that are able to consistently finish what they set out to do are able to accelerate at a faster rate, which is why it is so important for you to only be undertaking what you have proven to be capable of in previous sprints. It is what we refer to as implementing a pattern of 'yesterday’s weather'.
In my opinion this is a big downside.
The last time I checked, you can only size stories in a "Scrum" view. Teams that I work with that like the Kanban view have to create two boards from the same project in order to see the size information. It is a downside, since you can also not filter the control chart by story size. However, it may be possible to create a custom view and do these things, but it is not there out of the box. It is assumed that if you are using Kanban you don't size.