Time stop is a spell that stops time for other creatures, allowing one creature to take multiple turns in a row. It says:

You briefly stop the flow of time for everyone but yourself. No time passes for other creatures, while you take 1d4 + 1 turns in a row, during which you can use actions and move as normal.

Certainly, this is a magical effect. The spell causes the flow of time to stop for other creatures, and while you are taking multiple turns, no time flows for them. I imagine antimagic field can defeat it. The relevant text says:

Spells. Any active spell or other magical effect on a creature or an object in the sphere is suppressed while the creature or object is in it.

So, imagine combat between Annie, Tim, and Charlie. Ordinarily, initiative might look something like this:

Annie → Charlie → Tim

Suppose Annie casts time stop and rolled a 1 on their d4. Thus, they take 2 turns in a row. Initiative would look like this:

Annie → Annie → Charlie → Tim

Now imagine that Tim cast antimagic field, and following their turn, Annie casts time stop. Suppose they rolled a 1 on their d4 so that they can take 2 turns in a row. What would the initiative order look like?

Here are some possible resolutions I can think of, but none satisfy me totally:

1. Time stop defeats antimagic field. The initiative order is: Annie → Annie → Charlie → Tim. The reason this is unsatisfactory is that time stop shouldn't seem to prevail because it's a spell, and antimagic field defeats spells.

2. Time stop cannot be cast while there is an active antimagic field, because there exists some creatures you can't stop time for. The reason this is unsatisfactory is there is no rule that prevents these two spells from being active at the same time. Also, since things like beholders exist, it's not unreasonable to say there is almost always an active area of antimagic somewhere in the world, and that means time stop can almost never be used.

3. The caster of time stop and antimagic field take their turns as normal while everyone else is frozen in time. Thematically and narratively, this seems the most logical. So we go through the turn order, treating every turn Alice would have taken as one full round. For this scenario, since Alice takes two turns in a row, then we can imagine two rounds going by. Ordinarily, everyone but Alice takes a turn, but now we unfreeze anyone inside an area of antimagic. So initiative would be: Annie (time stop starts) → Charlie (frozen in time) → Tim (unfrozen) → Annie (time stop ends) → Charlie → Tim. The reason this is unsatisfactory is because we're advancing the "round count" now, which feasibly triggers things like lair actions that activate on a certain initiative count. It does have the side effect of allowing Tim to act normally though, affecting other creatures if he wants, because he isn't bound by time stop and Annie isn't the one doing the violations of the rules of the spell.

4. There is no answer to this question, and this is solidly in the zone of DM adjudication. This is unsatisfactory because, well, all questions answered that way tend to be unsatisfactory.

So which is it? Or is it an option I haven't listed here? Can Tim take turns as normal while inside an antimagic field if Annie casts time stop?