Look up and follow the time tested and proven method of artificially swarming using the Padgen method.
Several requirements or outcomes:
Queen (almost) starts brooding afresh.
Flying bees 'leave' with the queen.
Newly 'swarmed' colony makes a dreat deal of wax very quickly. Good for comb changes.
Old colony is depleted of flying bees on two occasions, once to 'swarm' with the queen and secondly to avoid cast swarms if two queen cells are left behind. Transfer of flying bees aids continued honey collection in the 'swarmed' section.
Any honey supers go with the queen so they are filled as a continuous process (no flying bees, let alone foragers, are left with the parent colony).
Colonies are kept adjacent for subsequent unification when the new queen is proven good, if colony number limits are to be adhered to.
Only the parent colony may need feeding, so no sugar syrup to the honey supers. That is assuming it is a productive stock that had got to the swarming stage, of course, and there is a reasonable nectar flow.
Parent colony will need minimum stores as open brood becomes capped.
There is a brood break in the parent colony which, nowadays, lends itself to easy varroa control if necessary.
The first capped brood in the swarmed section, if careful that only open brood is transferred at A/S, can be culled to reduce varroa in that part, too.
A far better system than most of the so-called modified methods. Proven to work, only needs the new brood box (with crownboard, roof, floor, frames and foundation), has no drawbacks like most of the others, which tend to be a compromise on one facet or another. It also needs no modifications by inexperienced beeks who then often finish up on the forum pleading for help when everything goes ---- up.
Splitting for increase needs to be done at around the same time and is different than, or separate to, the A/S. So many of the inexperienced and/or newbies try it far too early and end up on the forum asking for help with queens that are not getting mated optimally, or too late and finish up on the forum complaining about wasps! Demareeing is a good way as it is fairly well under the control of the beek as regards timing.
RAB