Can I create HTML custom field in JIRA (I need to display a table)?
No (at least not without some kind of add-on).
The reason this does not come out of the box and the reason I would suggest against looking into it further is that it's a significant security risk. It could allow for the malicious injection of scripts that could steal your information.
Have you tried to make the table in Wiki markup? That's allowed in multi-line text fields in Jira.
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