Unearthed Arcana has taken up the concept of Psionics several times now. At first, with some basic rules for a Mystic class up to level 5 (which I can't seem to find online anymore, they seem to have been removed), then an expansion up to level 10 for that class based on previous feedback, and finally the complete Mystic class.
The second version mentions:
Psionics and magic are two distinct forces. In general, an effect that affects a spell has no effect on a psionic effect. There is one important exception to this rule. A psionic effect that reproduces a spell is treated as magic. [...]
However, the revised, third version states the following:
As a student of psionics, you can master and use psionic talents and disciplines, the rules for which appear at the end of this document. Psionics is a special form of magic use, distinct from spellcasting.
Now, Psionics count as a form of magic, it's just different from Spellcasting - but what is Spellcasting? Is it the class feature of e. g. Wizards or Sorcerers, which means a Warlock's Pact Magic does not fall into this category either? Or is it simply the ability to cast spells, which would include warlocks but (mostly) exclude Mystics?
For the sake of this question, let's assume the latter.
Later on in version 3, the section Combining Psionic Effects states:
Combining Psionic Effects
Psionics and spells are separate effects, and therefore their benefits and drawbacks overlap. A psionic effect that reproduces a spell is an exception to this rule.
Therefore, the question remains:
Would an Antimagic Field affect someone wielding psionic powers, such as a Mystic?