An aura of antimagic surrounds you in 10-foot Emanation. No one can cast spells, take Magic actions, or create other magical effects inside the aura, and those things can’t target or otherwise affect anything inside it. Magical properties of magic items don’t work inside the aura or on anything inside it.
Areas of effect created by spells or other magic can’t extend into the aura, and no one can teleport into or out of it or use planar travel there. Portals close temporarily while in the aura.
Ongoing spells, except those cast by an Artifact or a deity, are suppressed in the area. While an effect is suppressed, it doesn’t function, but the time it spends suppressed counts against its duration.
Dispel Magic has no effect on the aura, and the auras created by different Antimagic Field spells don’t nullify each other.
* - (iron filings)
So, I don't think that any spells/AOE would be able to target anything inside of an antimagic field, nor would anything inside of an antimagic field be able to target anything outside. However, wouldn't the caster of the Antimagic Field spell be able to cast spells on themselves? If an Emanation moves with the creature that is its origin, and an Emanation's origin (the caster) isn't included in the area of effect by default, does that mean that any spell that never attempts to pass through the field would work (such as Shield)? I still don't think spells with a range of Touch would work on either party, as no matter how close you get to a target, you can't literally merge into their being, but I think RAW, spells with a range of Self should work!
Psychic blades are explicitly magical. They will not function within an anti-magic field.
You can manifest shimmering blades of psychic energy. Whenever you take the Attack action or make an Opportunity Attack, you can manifest a Psychic Blade in your free hand and make the attack with that blade. The magic blade has the following traits: