A K-4 visa is a derivative visa of a K-3 visa for unmarried children under the age of 21. Before a K-4 visa can be issued to a child, the parent must have a K-3 visa or be in K-3 status.
The process begins the filing of an immigrant Petition for Alien Relative, Form I-130 for your spouse and children. The USCIS will send you a Notice of Action (Form I-797) receipt notice after filing of the petition.
After you have receiving the receipt notice, you should file the Petition for Alien Fiancé (Form I-129F) for your spouse and children. The I-129 Form, Petition for Alien Fiancé is used to obtain a K-3 visa for your alien spouse.
The foreign spouse will go to a US embassy and apply for the K-3 visa, and a K-4 visa for her children. If the K-3 visa is issued by the U.S. Embassy, the foreign spouse may enter into the U.S. with a K-3 and their children can enter the U.S. on a K-4 visa. After entry into the United States, an immigration petition will have to be filed for the K-3 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.
If the immigrant parent adjust status, they will no longer be in K-3 status, therefore, the child will no longer be in lawful K-4 status. Since the K-4 status is merely a derivative classification, and that child would begin to accrue unlawful presence.
To apply for a K-4 Visa in Thailand, please visit this page.