I need to understand whether the focus should be on one person at a time in such experimental designs. Kindly help me with the references if possible. Thank you.
If you implement the same procedure for all of them with the same goal, this is called multiple baseline across participants design. You focus of course on all of them individually, not only on one child.
Preferably you will be doing the intervention with each child separately, not to have other variables affecting treatment (like other kids present etc.).
If you planned to do the treatment separately with all kids already, and your question refers to doing it at the same time, or one after the other (for example each month with one child), it is totally up to you and your time management possibilities.
Yes, it is possible to start the clinical intervention together for all four participants in a single case experimental design (small n design). However, it is important to consider the specific research goals and objectives when designing the study.