Xjyuk

I have a niece who is divorced and we want her to get rehabilitated and one possibility is that she may marry a USA citizen. She has a 11-year-old son from a previous marriage. I looked in Google Search to find a general answer (there is no prospect yet, so there is no point in going to an immigration lawyer). She does not want to get separated from her son.

You haven't actually asked a question, but I presume that you want to know how the 11-year-old son could accompany his mother to the US if she moves to the US as the fiancée or spouse of a US citizen.

The US Department of State has a page about this on their site. It says:

Overview: What Is a K-1 Visa?

The fiancé(e) K-1 nonimmigrant visa is for the foreign-citizen fiancé(e) of a United States (U.S.) citizen. The K-1 visa permits the foreign-citizen fiancé(e) to travel to the United States and marry his or her U.S. citizen sponsor within 90 days of arrival. The foreign-citizen will then apply for adjustment of status to a permanent resident (LPR) with the Department of Homeland Security (DHS), U.S. Citizenship and Immigration Services (USCIS). Because a fiancé(e) visa permits the holder to immigrate to the U.S. and marry a U.S. citizen shortly after arrival in the United States, the fiancé(e) must meet some of the requirements of an immigrant visa. Eligible children of K-1 visa applicants receive K-2 visas.

Later, it says:

Does My U.S. Citizen Fiancé(e) Need to File Separate Petitions for My Children?

No. Your eligible children may apply for K-2 visas based on the approval of Form I-129F, Petition for Alien Fiancé(e), that your U.S. citizen fiancé(e) filed on your behalf, but your U.S. citizen fiancé(e) must list the children on the petition. Separate visa applications must be submitted for each K-2 visa applicant, and each applicant must pay the K visa application fee.

After your marriage, your children will need to file separately from you for adjustment of status. They cannot be included on your application for adjustment of status. More information about adjustment of status is available on USCIS’s website under Green Card (Permanent Residence).

Important Notice: Under U.S. immigration law, a child must be unmarried. In order to file for adjustment of status for your child following your marriage to your U.S. citizen spouse, the child’s stepchild relationship with your spouse must be created before the child reaches the age of 18.

(Emphasis and links in the original have been removed.)

If she marries before moving to the US, then the process is somewhat different, but it is still possible for minor children to be included. You can read more about that at Immigrant Visa for a Spouse of a U.S. Citizen (IR1 or CR1).