A braid is by definition made up of three cords (at least), while what you ask for is made by two cords, so i think that it’s not possible to get with particle children which are created automatically by three cords for each strand.
thanks for the reply, but it seems that i had a little misunderstanding in my explanation: What i am trying to achieve is a SIGNLE Cord braid. Just a bundle of hair, twisted around an axis - similar to the screw modifier for meshes, but only to twist hairs. The desired result does not necessarily to be achieved using the braid function - maybe there is another way or setting using a modifier or force field - i tried force fields also, but until now i did not get any result.
The idea has also to not to create only one Single Cord braid, but a bunch of it (say 100 or more).