Only spouses of a U.S. citizens may be issued a K3 visa. Unmarried children under 21 of the K3 visa holder are eligible for a K4.
A K4 visa for are unmarried minor children of a K3 visa. The K4 visa allows children of a K3 visa holder to travel with them to the United States.
The K4 visa is part of an application for K3 visa. The Petition for Alien Relative (I-130) must include the names children applying for K4 visa. The I-129F Petition must also include the names of the children.
Once the I-129F petition approved, the relevant documents will be forwarded to the National Visa Center (NVC) for processing. Subsequently, the NVC will send the case to the U.S. Embassy.
The U.S. embassy will notify the beneficiaries that the documents pertaining to their application are received. Subsequently, a consular interview will be conducted with the beneficiaries.
Note that a child of a U.S. citizen petitioner is not eligible for a K4 visa unless that child is also a derivative child of an eligible K3 spouse. Unlike the K3, the K4 is not a close substitute for an IR2 immigrant visa.
The K-4 child will not be able to file for adjustment of status in the United States until the U.S. citizen parent/step-parent files a I-130 on behalf of the child. When the immigrant parent adjusting status, they will no longer be in K-3 status. Therefore, the child will no longer be in lawful K-4 status, since this is merely a derivative classification, and that child would begin to accrue unlawful presence.
K3 and K4 status holders can travel outside the United States and return on their visa without fear of their adjustment of status being deemed abandoned.
See the US Visa Application in Thailand: Complications And Supported Help page.