Any creature created by magic with a non-instantaneous duration disappears
The official D&D Sage advice compendium contains the following clarification:
Whenever you wonder whether a spell’s effects can be dispelled or suspended, you need to answer one question: is the spell’s duration instantaneous? If the answer is yes, there is nothing to dispel or suspend.
The clarification continues to explain an example of this at play: the spell conjure woodland beings. Conjure Woodland Beings has a non-instantaneous duration, so the magic that summons the creatures is acting upon them and maintaining their presence for the whole duration of the spell. When they enter an anti-magic field, the magic that is keeping the summoned creatures in place is suspended, so the creatures disappear.
When this situation occurs, ask yourself whether or not the effect that summoned the creature is instantaneous. If it's instantaneous, then the creature will stay, otherwise it will disappear while its space is within the field.
To address your examples
Elementals and fiends will only disappear if the spell that summoned them is not instantaneous. A spell like conjure elemental falls into this category. However, a spell like planar ally can summon an elemental or fiend and has a duration of instantaneous. So a creature summoned by that spell will not disappear.
In general undead and constructs follow the same rule as any other creature. Unless the magic that created it is non-instantaneous, a construct or undead can enter an antimagic field with no ill effect (barring any specific exceptions from some other source: like that creature's stat block).