If you have a nonmagical "Magic of meaning" ability, for example. of Chuul, but they are inside an antimagic field, can you detect magic (which is out of the field)? The skill states:
The chuul feels magic at 120 feet from her at will. This feature otherwise works like the magic spell of detection but is not magical in itself
So that means that this trait would not be nullified by an antimagic field.
Detect magic itself has 2 parts, first "feel the magic" and, secondly, see its aura:
For the duration, you feel the presence of magic 30 feet away from you. If you perceive magic in this way, you can use your action to see a weak aura around any creature or object visible in the area that contains magic, and learn its magic school, if there is one.
The spell can penetrate most of the barriers, but is blocked by 1 foot of stone, 1 inch of common metal, a thin sheet of lead or 3 feet of wood or dirt.
Now, the Antimagic Field (the spell) states that:
This area is divorced from the magical energy that the multiverse infuses. Within the Sphere, the spells can not be cast, the summoned creatures disappear and even the magical Objects become mundane.
Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the Sphere and can not excel in it.
So, the magic auras, which Detect Magic allows you to see, could reach you while you're inside the field? I really could not find a RAW definition of whether these auras count as a "magic effect," or if they are essentially a non-magical energy emission that you can not normally see, and detecting magic simply expands you. Rank to cover it.
And the first part, that of feeling magic in the first place, is completely left to our imagination, but most likely there is some kind of emanation that has to come back to your player, so the same question arises.